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Paper Citation Record · LEDGER

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow

As of 14 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 1 inbound Pith citation observation for arXiv:2506.23359.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.23359 v1

Coverage vector

measured 67 of 67 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:00:38.203994Z

measured 68 of 68 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:45:39.782324Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-06T22:45:40.635468Z

Reference resolution

67 of 67 outbound references displayed

  • verified exact6
  • verified fuzzy54
  • unresolved7
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d280941b-91ea-4619-85b7-e040efa6526f · outbound

This paper cites The `Holiverse': holistic eversion of the 2-sphere in $\R^3$.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow The `Holiverse': holistic eversion of the 2-sphere in $\R^3$

Reference 1

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:00:38.965042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.196904Z digest=sha256:522396b87567234767cc8dff7513d30df771cfc838c99c5ba8c7fa1caf005af0

Observation 679dfc66-d10f-4d9a-9e9f-6318b811b62e · outbound

This paper cites An algebraic halfway model for the eversion of the sphere.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow An algebraic halfway model for the eversion of the sphere

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:48.549961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.309463Z digest=sha256:0fc96374e1b5d71db95f2d8087344eaea2dcaacfbf5ac0b02b69ea7341e61bd9

Observation 164b8fcc-f99e-4b34-9312-4b7b469a1b0d · outbound

This paper cites Analytic sphere eversion using ruled surfaces.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Analytic sphere eversion using ruled surfaces

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:48.509742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.382847Z digest=sha256:e913f3c2a709f4c1a2b5139c4d2ef4d4b539a139589047b86125a7bba225db8e

Observation 353132cb-699f-42d1-b8b4-89c46afb8a33 · outbound

This paper cites Existence of minimizing W illmore surfaces of prescribed genus.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Existence of minimizing W illmore surfaces of prescribed genus

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:48.273340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.440447Z digest=sha256:911e4f0cfed2957eafa9bad2fc2ba4b59b002d240657445a40cef400f5d4ef2d

Observation bba9d0ac-81cc-4aa0-8295-e995076221f1 · outbound

This paper cites Polygon Mesh Processing.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Polygon Mesh Processing

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:48.102496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.524099Z digest=sha256:1909005e681ff22c683d901877f5f8eef102a0064dc3fff2be6bb946ca7cb35c

Observation 820d45e9-d291-444d-8cdf-ae1bfe3a5c42 · outbound

This paper cites A singular example for the W illmore flow.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow A singular example for the W illmore flow

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:47.873540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.607832Z digest=sha256:de36233872693a02dce3bbec7032065b7bcf2837632d2040d104a4528ef9ff8d

Observation b9e99bfb-d18f-4624-b6b4-3fc88cdd17c5 · outbound

This paper cites Energy quantization for W illmore surfaces and applications.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Energy quantization for W illmore surfaces and applications

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:47.709332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.673615Z digest=sha256:52f048f0d244687060f3470f701c5cf53487bb77f12ac80807d2529a37b4a332

Observation b255b657-1bbe-4ff7-a31c-579e1740f8e0 · outbound

This paper cites Immersions with bounded second fundamental form.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Immersions with bounded second fundamental form

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:47.547079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.840392Z digest=sha256:f13ffad2a66319befa5f0709cd898c6e891caa7c68d86bc4225eafef079fa61d

Observation 40a983da-a8bd-496d-a1e9-9b4ec8d6de10 · outbound

This paper cites an unresolved cited work.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:00:47.405034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:33.916791Z digest=sha256:f5cd9159c21cedb2e591d766e30c4e3b750657c4d92878decd039d6cf55c8387

Observation 83e387e6-a2e7-4134-b4a8-e39044e17b6c · outbound

This paper cites Bubble tree of branched conformal immersions and applications to the W illmore functional.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Bubble tree of branched conformal immersions and applications to the W illmore functional

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:47.261398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.006347Z digest=sha256:f65265a19d7fd8088bfe81342bfaf06b674b0cb295b89a0c6eba2113d2ccb1e6

Observation c30a9a69-5aaa-447a-bb9d-02c36e7bc697 · outbound

This paper cites do Carmo.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow do Carmo

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:47.136823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.104827Z digest=sha256:b12594ad8c31f6614a78534901db48783754e6f73ab80695b72fd6bee30e6d70

Observation 13a2f884-99ce-4e33-93e8-193e6f98611d · outbound

This paper cites Dimension reduction for Willmore flows of tori: fixed conformal class and analysis of singularities.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Dimension reduction for Willmore flows of tori: fixed conformal class and analysis of singularities

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-06T22:00:34.198717Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T22:00:34.198717Z digest=sha256:9113b31e77ed909e92f5b648d5ecd25b5d171ad42d10d9bf8db9f14441c89343

Observation 60bb94ed-610f-4a94-be24-636182181205 · outbound

This paper cites uller, Reiner Sch\.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow uller, Reiner Sch\

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:47.020114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.287071Z digest=sha256:b8a18b231385952c9a5e13fa23066e81a2bdff0f953c1d3eb6f343fbc1205193

Observation f788a952-e1c1-433e-af44-4c2acf10f2f8 · outbound

This paper cites Francis and Bernard Morin.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Francis and Bernard Morin

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:46.912659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.446389Z digest=sha256:79056b22fecb41ab4c3560dd407ed755f6b722f62fd8145ab7da5a2f897b4f6f

Observation 279bb884-5843-44a2-a91e-7c4a2ce8dd38 · outbound

This paper cites Sullivan, and Chris Hartman.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Sullivan, and Chris Hartman

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:46.792183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.572197Z digest=sha256:8e2f16afcf0776a6eac1fed577a93b20d7e3ea63f4f8ec614e4d0583676d1dfd

Observation a5c61c0b-67ad-462b-950f-5be26da01c73 · outbound

This paper cites Sullivan, Rob B.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Sullivan, Rob B

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:46.697222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.700989Z digest=sha256:174e04c6388a421c48a0bcc7a93c1fc4b30013400288f277d6ee1452db9e1644

Observation 944664cd-5ac1-4bbe-8577-30dd4f369763 · outbound

This paper cites Goryunov.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Goryunov

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:46.600899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.796921Z digest=sha256:d4b9c78999e992079cf3abb3d5da0c70a4d9887b6dce5a462a28f71baf933d0f

Observation 51a66043-0693-4372-89a2-4445cac012de · outbound

This paper cites Helfrich.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Helfrich

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:46.456988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.865365Z digest=sha256:1bfdd9dcfa4f4cbd8178fbd36639c6896db59dd52a37b54412846ba2ff8562a4

Observation dddcb71a-f8c3-4f26-b068-84b00bc017b8 · outbound

This paper cites Geometry of complete minimal surfaces at infinity and the W illmore index of their inversions.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Geometry of complete minimal surfaces at infinity and the W illmore index of their inversions

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:46.285483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:34.956933Z digest=sha256:130ef97f230e40579d5776c3b4c03123af0c0ce6b462ae96e2b2e8ab0609ab1f

Observation 99536947-1f4e-468f-8470-3e37bd8b1e8e · outbound

This paper cites On the index of W illmore spheres.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow On the index of W illmore spheres

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:46.123662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.113574Z digest=sha256:b630353f8cdd1b8dfdde35b712f8c19baae59a69d14684e64cce311beb10ad53

Observation 0640d6ab-b406-4e83-b9fa-e1038e1d72bc · outbound

This paper cites an unresolved cited work.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:00:45.939561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.145313Z digest=sha256:fa6acb87a2837565ddccdbeaed84e8845400564d49e73edb2256e11fcbb704dc

Observation e277a28b-4d5f-404c-bd52-043f534cf33b · outbound

This paper cites Sphere eversion from the viewpoint of generic homotopy.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Sphere eversion from the viewpoint of generic homotopy

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:45.805337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.231709Z digest=sha256:34d119e1d4790bb946f50a4f1057129da3c7ab96e8eecc3736b8b6fb2919f820

Observation 0300ba61-a499-470f-a5c1-605f13ab9e23 · outbound

This paper cites W^ 2,2 -conformal immersions of a closed R iemann surface into R^n.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow W^ 2,2 -conformal immersions of a closed R iemann surface into R^n

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:45.648249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.318298Z digest=sha256:8c7993da9a8a8714fd249df871e4d816e0f4acf61ddb1b674980b12b2dec274b

Observation 6ceffb61-8c1c-4b3f-931f-ca6c806fc63e · outbound

This paper cites The large genus limit of the infimum of the W illmore energy.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow The large genus limit of the infimum of the W illmore energy

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:45.477261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.392888Z digest=sha256:0e57d8f29b2d7a7b0e6e026f814dd717f21aa3c72d8e1d034633328ad0667499

Observation a985cc9a-94ef-4406-a3a8-5d86894e4fdd · outbound

This paper cites The area preserving W illmore flow and local maximizers of the H awking mass in asymptotically S chwarzschild manifolds.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow The area preserving W illmore flow and local maximizers of the H awking mass in asymptotically S chwarzschild manifolds

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:45.286369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.451356Z digest=sha256:1d0d573f6d24275bd1ac2235334f3f1a44b57cbbbdf259e04d0a6623678c9a43

Observation 76bcaf90-8897-485c-954b-969aa1a519c9 · outbound

This paper cites The W illmore flow with small initial energy.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow The W illmore flow with small initial energy

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:45.123409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.546128Z digest=sha256:91477bd38d32fe66698e8a9138532eecc86dc757dfe19701ff64d5802ea0cd6e

Observation f98316f7-b3b2-4c4f-a682-ab43e42f51f3 · outbound

This paper cites Gradient flow for the W illmore functional.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Gradient flow for the W illmore functional

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:44.924033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.630150Z digest=sha256:fd76ab8282f2b21015d03ad59393305299acb360f1a79d2f9bd009d506b3b542

Observation 3e58dfdc-c051-47d8-9f85-56ecc9490b46 · outbound

This paper cites Removability of point singularities of W illmore surfaces.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Removability of point singularities of W illmore surfaces

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:44.710460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.712879Z digest=sha256:c908a426fedf8a9893425327c35777c67b7829642703a3cbe2872529150e7538

Observation 6ae8ea75-b45d-4ddb-a613-39e175a7fcbd · outbound

This paper cites The W illmore functional.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow The W illmore functional

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:44.511771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.789696Z digest=sha256:0da4e7511b6713b236f25e66e39b785d38851dc2688b12e92a65651493eb0aab

Observation b369d824-bf41-4767-9a1c-88d2f3e22609 · outbound

This paper cites an unresolved cited work.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:00:44.321904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.864764Z digest=sha256:9bdb70e8411efc5be9d165dd1203977001df731ef6ad4c56c46387e5a3526e75

Observation ce371b7f-c241-4975-8999-6d2e5c718a55 · outbound

This paper cites Conformal geometry and complete minimal surfaces.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Conformal geometry and complete minimal surfaces

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:44.166395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:35.930854Z digest=sha256:a0eb9d05108b937461cc1455212399c9c7e6a873b2b696c3540a157dc70e3205

Observation e67c4652-60b8-4790-afd9-a05fa75b9538 · outbound

This paper cites Bubbles, conservation laws, and balanced diagrams.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Bubbles, conservation laws, and balanced diagrams

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:43.981035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.009807Z digest=sha256:9b9f3209edcc3980cb0f816f42cc3e945ae30bed656a6cd5a8955092994207a1

Observation 106e9e14-92c1-40ab-940d-2cbcdb84bf2c · outbound

This paper cites A compactness theorem for surfaces with L_p -bounded second fundamental form.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow A compactness theorem for surfaces with L_p -bounded second fundamental form

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:43.798960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.070241Z digest=sha256:640625759f257a2edbd1785fc305cfa5d4e560910b406681f339751349273851

Observation e0733c88-d0f0-444b-ac19-478b822ae7c0 · outbound

This paper cites Branched W illmore spheres.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Branched W illmore spheres

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:43.658323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.122168Z digest=sha256:c765bff99157ce65c61c1fe7731391dc8867bfd0bfa6010b52b6e73a1fc74342

Observation 39d39ac0-b17b-405b-98b7-098d4881a8df · outbound

This paper cites L \'o pez.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow L \'o pez

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:43.500006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.190658Z digest=sha256:aeca1ce8afeafc1afe925f5bbc3767f41a0080d0edc2d003f05673b4253d85ed

Observation 1df05cb6-430b-4559-806f-8e76174864d6 · outbound

This paper cites Curves in the hyperbolic plane and mean curvature of tori in 3 -space.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Curves in the hyperbolic plane and mean curvature of tori in 3 -space

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:43.338322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.259211Z digest=sha256:c2ec9f5990e60bc918a643b81677a0fd8948df3f8c4a33c3b3f8fb52efdf6fc8

Observation 2852a44f-b0f7-41c0-ab3d-8fa502e9780f · outbound

This paper cites A new conformal invariant and its applications to the W illmore conjecture and the first eigenvalue of compact surfaces.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow A new conformal invariant and its applications to the W illmore conjecture and the first eigenvalue of compact surfaces

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:43.163884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.337317Z digest=sha256:edf113abe4fc6ed0ff04de6d4398f6de34fa82b4cda59611926d53ab16753223

Observation e0a3aa5f-50e6-4693-9d9a-023ac6fbb43a · outbound

This paper cites Closed mean curvature flows with asymptotically conical singularities.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Closed mean curvature flows with asymptotically conical singularities

Reference 38

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:00:38.831175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.422691Z digest=sha256:7333bf5c566d3e5665e02fece4234912444134a5f8f3803492f4cfe0b1ff7fc3

Observation dd532b2d-a77e-4279-b552-4128bbd8f5ae · outbound

This paper cites Explicit formulas, symmetry and symmetry breaking for W illmore surfaces of revolution.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Explicit formulas, symmetry and symmetry breaking for W illmore surfaces of revolution

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:43.056764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.501801Z digest=sha256:ccbd8be9fb3002720b456dfefca0e207ac65dad3c297aa7eb07c9e8d83692b4e

Observation 7b0d97f3-52eb-474c-ad76-01d3f3a27c95 · outbound

This paper cites Classification of branched Willmore spheres.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Classification of branched Willmore spheres

Reference 40

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:00:38.740413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.571825Z digest=sha256:964efc9cb18386aa90075e8e38c08fd9a03e41d503341d32a2ea684aa8c15b7f

Observation e02553dc-9c0f-4db0-99ab-d337c3f80fe9 · outbound

This paper cites Every sphere eversion has a quadruple point.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Every sphere eversion has a quadruple point

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:42.917758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.629857Z digest=sha256:d3afdb814a5e5004f094428c0248739af5da73865e783b2370b4cb228291745a

Observation 48590c0d-1083-4b83-9c58-40a3961d702f · outbound

This paper cites On the M orse index of branched W illmore spheres in 3-space.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow On the M orse index of branched W illmore spheres in 3-space

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:42.773360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.678929Z digest=sha256:2415b44484178442315c6db4ab716dde566b4896fac8bcaa515abdbb64dc4525

Observation 96337a08-1bfd-4810-af8b-36a24fc2b0e3 · outbound

This paper cites Li- Y au type inequality for curves in any codimension.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Li- Y au type inequality for curves in any codimension

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:42.613837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.732091Z digest=sha256:4c878fff1964fe7e3948432a454e6bb2ace41a3a68d9a4f16692f51dfa104e55

Observation 68c86b26-614a-4483-8a1c-a981756f810c · outbound

This paper cites Marques and Andr\'e Neves.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Marques and Andr\'e Neves

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:42.416317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.778719Z digest=sha256:276bf2630b2df0689eca4ad11ff69d54dc0fb35e89c206c2a8050b5db33f73f5

Observation bd4c49ee-e27f-496a-8724-bcfa4a403c5f · outbound

This paper cites Marques and Andr\'e Neves.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Marques and Andr\'e Neves

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:42.273141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.843086Z digest=sha256:20333c1c1161ae9029f88ec2fc1e6af9f9a4b5722639192e9e9e953adb1110ee

Observation 5e3732ee-daf2-4cfe-962b-3136f458053f · outbound

This paper cites an unresolved cited work.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:00:42.046198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.894198Z digest=sha256:37c6c1cb62a3892a62e9fe7946faf38f38e04f9f10a734bb06ee6872aa59a18a

Observation d9424de6-cbf9-4df1-a1bb-683281c56214 · outbound

This paper cites Le retournement de la sphere.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Le retournement de la sphere

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:41.794988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:36.935814Z digest=sha256:7a97db390e9bd3043bef500da78505b1e80575f88a32443bc07020a0fd54def0

Observation f6213b88-1fca-406d-b2ec-48b79fbb5183 · outbound

This paper cites Probl\'ematique du retournement de la sph\`ere.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Probl\'ematique du retournement de la sph\`ere

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:41.561778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.007174Z digest=sha256:7656b948ee1b199082f53ef958b0139a8f6f555b163b0fab8af8d2b91392cee8

Observation f41f1192-258d-450d-a2c7-ec7c685b2f29 · outbound

This paper cites The classification of branched W illmore spheres in the 3-sphere and the 4-sphere.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow The classification of branched W illmore spheres in the 3-sphere and the 4-sphere

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:41.402936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.092477Z digest=sha256:186a2d67cb7704697a80137e9a840f8c0249b59967d4ea8560864d0270d53fc8

Observation b9c5d21d-b1b2-40f5-be1f-eacf3dbcd966 · outbound

This paper cites A L i- Y au inequality for the 1-dimensional W illmore energy.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow A L i- Y au inequality for the 1-dimensional W illmore energy

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:41.219727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.192026Z digest=sha256:70e943a54ef4847e12153670aea486f0a353798792e74131680b939c5bf26513

Observation e72ea82d-5dbd-45ca-a01e-38887e619226 · outbound

This paper cites Short closed geodesics and the W illmore energy, 2025.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Short closed geodesics and the W illmore energy, 2025

Reference 51

Resolution
verified exact
raw_fallback, observed 2026-08-06T22:00:38.623864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.251075Z digest=sha256:056e19be251a30ef81061dc7151f8e9d618bdd4f73f3044464143a5b9d05ac49

Observation 951558b6-700b-4e45-a30f-9c494fa8feeb · outbound

This paper cites Mayer and Gieri Simonett.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Mayer and Gieri Simonett

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:41.052190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.301227Z digest=sha256:265924c514e551d9d982cf62038fd9233af734aa89832a1fb2f58feb972aea24

Observation cb980b72-9268-46b4-aa2c-4344385c6fd0 · outbound

This paper cites Elasticity Theory After Germain , pages 103--114.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Elasticity Theory After Germain , pages 103--114

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:40.760189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.367387Z digest=sha256:0fb2580faa463f69e70b0287269d35caa7d9f9e12621a5089d2e2cf2350be694

Observation e811c902-58c6-47b1-b6fa-b3830f0a5a47 · outbound

This paper cites Riemann bilinear relations on minimal surfaces.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Riemann bilinear relations on minimal surfaces

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:40.558396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.423418Z digest=sha256:a2cc0445207ff671debe1109937c246708e5cd4887f5e9df8c2458bdd7a7c5b7

Observation 7ca2235a-9abd-4688-95ab-36b6aebea7fb · outbound

This paper cites Turning a surface inside out.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Turning a surface inside out

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:40.269091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.489475Z digest=sha256:35305021f240c1ca3d9698b0a1555f345e99d7963064fc15f527482f7feae9df

Observation db720b7d-8a85-4306-b627-036ec6644a96 · outbound

This paper cites The parametric W illmore flow.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow The parametric W illmore flow

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:40.046395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.526848Z digest=sha256:02513d385d544cb38b6db9078a05c245fec2ca13ec570e690317c314cd95d4fe

Observation 972b7f8b-1094-4ed9-9a93-d7a8058aa2a2 · outbound

This paper cites Pinkall and I.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Pinkall and I

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:39.883357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.600270Z digest=sha256:85b6b2d5d96bf6b687f67b44b502fcf10380e36716509609d367c4251fd3051d

Observation c3b85bf8-c069-49dc-8de6-de79045ad2a7 · outbound

This paper cites Analysis aspects of W illmore surfaces.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Analysis aspects of W illmore surfaces

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:39.723446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.639757Z digest=sha256:02913fb310a456284a3cac6a17099dc47496e7591b6eb784afe6cab25e878808

Observation 459d1107-0bc0-489d-a404-3f51009b5353 · outbound

This paper cites Conformally Invariant Variational Problems.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Conformally Invariant Variational Problems

Reference 59

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:00:38.448708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.731539Z digest=sha256:d668c8146993bae63987b09fba53241df544287fcfc9aeb0290767a761e345a1

Observation cfb97ddb-7e6a-457f-9420-8a228b81d716 · outbound

This paper cites Willmore minmax surfaces and the cost of the sphere eversion.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Willmore minmax surfaces and the cost of the sphere eversion

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:39.559952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.820468Z digest=sha256:b4038270e4cdee28b960f6d330fe6975051c552339b27b93a0d7bd21b7b03d0c

Observation aaec7e09-8654-4acc-8d32-95030f0c6d76 · outbound

This paper cites Global existence for the W illmore flow with boundary via S imon's L i- Y au inequality.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Global existence for the W illmore flow with boundary via S imon's L i- Y au inequality

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:39.435480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.873880Z digest=sha256:ff7b69a4849af869bf46c0147518e41a7064bb3a12cc09920ce7e5cb01115a1b

Observation 6b6f57ea-ffa9-4fcd-bc11-ed7256a0e842 · outbound

This paper cites An Invariant for Triple-Point-Free Immersed Spheres.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow An Invariant for Triple-Point-Free Immersed Spheres

Reference 62

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:00:38.352454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.914547Z digest=sha256:6c6aa38f319057f1dd4413db083f89a77784c921038114603f0b85955b4db2e8

Observation e14e9ed5-a2c6-4005-ac0c-4c40ad73f80d · outbound

This paper cites Existence of surfaces minimizing the W illmore functional.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Existence of surfaces minimizing the W illmore functional

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:39.283111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:37.990892Z digest=sha256:3b4a04738dfcd81f8163c2525fdbb11da95f1b44dfe53e6a15c604b758371fab

Observation dabb2815-049a-4d47-9b4e-39a2bfaf8007 · outbound

This paper cites The W illmore flow near spheres.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow The W illmore flow near spheres

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:39.137531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:38.044984Z digest=sha256:195fee97b8a879bc01141244dadd9868c0ab0e02e59a3d17ca851132a5852ac6

Observation aaee6417-804f-4e81-b3b3-69b92c8831fd · outbound

This paper cites A classification of immersions of the two-sphere.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow A classification of immersions of the two-sphere

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:00:39.051792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:00:38.107647Z digest=sha256:71143d329ef1496b0435f5a90efe56d9aeeeabc2550bb9dca2347f58f7b8c283

Observation 69e97431-729d-42b0-9221-4d5024e24f81 · outbound

This paper cites Diffeomorphisms of the 2 -sphere.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Diffeomorphisms of the 2 -sphere

Reference 66

Resolution
unresolved
no resolver link, observed 2026-08-06T22:00:38.152903Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T22:00:38.152903Z digest=sha256:dbc18454bcd6b4b9796735ddacc2026d2a073a7fd7055ec111709b2ebe3a4545

Observation f8fc409b-195a-4919-a58d-f8ec4b32e347 · outbound

This paper cites Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers.

The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers

Reference 67

Resolution
unresolved
no resolver link, observed 2026-08-06T22:00:38.203994Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T22:00:38.203994Z digest=sha256:65db6e9a610966d240260e6868125e165b4cd481c9c2c6b68d87efd4449eb6ba

Pith citing papers

Observation 139ec1cd-17db-409e-b512-d60a2b29885a · inbound

An Invariant for Triple-Point-Free Immersed Spheres cites this paper.

An Invariant for Triple-Point-Free Immersed Spheres The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:45:40.691505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-08-06T22:45:39.782324Z digest=sha256:4b980d6f517cef926180adb7f09b2d4071e1fb11c6ac37069f79b3b201b3be4f