Paper Citation Record · LEDGER

Singularities of mean curvature flow with bounded mean curvature and Morse index

As of 13 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2501.05489.

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pith.paper-citation-record.v1
2501.05489 v3

Coverage vector

measured 41 of 41 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-10T21:35:04.534618Z

measured 41 of 41 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

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Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

41 of 41 outbound references displayed

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verified fuzzy31
unresolved6
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External citation measurements

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Outbound references

Observation c1fb0687-a705-4843-ae03-9fec009200d8 · outbound

This paper cites Allard, On the ﬁrst variation of a varifold, Ann.

Singularities of mean curvature flow with bounded mean curvature and Morse index Allard, On the ﬁrst variation of a varifold, Ann

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.372947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9ad48ca5-8638-40a6-9cfe-f6d5587f8d29 · outbound

This paper cites Type II smoothing in mean curvature flow.

Singularities of mean curvature flow with bounded mean curvature and Morse index Type II smoothing in mean curvature flow

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-10T21:35:04.815659Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f8710f9e-4518-43a1-8bd7-a954d19dbc76 · outbound

This paper cites an unresolved cited work.

Singularities of mean curvature flow with bounded mean curvature and Morse index Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:35:05.356327Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8e0f4696-f93b-4ab6-ad4b-80da92f177dd · outbound

This paper cites Andrews, Noncollapsing in mean-convex mean curvatur e ﬂow, Geom.

Singularities of mean curvature flow with bounded mean curvature and Morse index Andrews, Noncollapsing in mean-convex mean curvatur e ﬂow, Geom

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.338974Z

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Observation ee36b894-2c33-47bb-b7a3-087251a0c0aa · outbound

This paper cites On the Multiplicity One Conjecture for Mean Curvature Flows of surfaces.

Singularities of mean curvature flow with bounded mean curvature and Morse index On the Multiplicity One Conjecture for Mean Curvature Flows of surfaces

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T21:35:04.317152Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e94a45b-c220-4907-801c-a06be4da7f43 · outbound

This paper cites Brakke, The motion of a surface by its mean curvature, Mathematical Notes, Princeton University Press(1978).

Singularities of mean curvature flow with bounded mean curvature and Morse index Brakke, The motion of a surface by its mean curvature, Mathematical Notes, Princeton University Press(1978)

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.322996Z

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Observation 62c21df4-db17-48d4-b9d7-28d87a97480f · outbound

This paper cites Chodosh, K.Choi, C.

Singularities of mean curvature flow with bounded mean curvature and Morse index Chodosh, K.Choi, C

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T21:35:04.331971Z

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Unavailable: canonical work link unavailable.

Observation 82032394-a079-48ee-a279-690649f2bc8e · outbound

This paper cites an unresolved cited work.

Singularities of mean curvature flow with bounded mean curvature and Morse index Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:35:05.302064Z

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Observation 5052214d-be75-4c7a-a7e4-86ab01a1e368 · outbound

This paper cites Cheeger, R.

Singularities of mean curvature flow with bounded mean curvature and Morse index Cheeger, R

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.284182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation abb52207-5060-4519-b6f4-a4dd69e98829 · outbound

This paper cites Colding and W.

Singularities of mean curvature flow with bounded mean curvature and Morse index Colding and W

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.264534Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f84d79f1-dce7-4d94-bd2c-e51ed0b92766 · outbound

This paper cites Colding and W.

Singularities of mean curvature flow with bounded mean curvature and Morse index Colding and W

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.247429Z

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Observation 2c9ecf7e-5e3b-4270-a137-ea006929f52b · outbound

This paper cites Colding and W.

Singularities of mean curvature flow with bounded mean curvature and Morse index Colding and W

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.230425Z

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Observation 7f77432a-e701-4eb7-9260-ac0ea69fdd2d · outbound

This paper cites A strong Frankel Theorem for shrinkers.

Singularities of mean curvature flow with bounded mean curvature and Morse index A strong Frankel Theorem for shrinkers

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-10T21:35:04.670752Z

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Observation cbc86f39-96da-489d-8684-39c121179ef9 · outbound

This paper cites Cheeger and A.

Singularities of mean curvature flow with bounded mean curvature and Morse index Cheeger and A

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.215445Z

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Observation 3f08cfad-c550-45bd-bffb-c891fd5f832c · outbound

This paper cites Chodosh and F.

Singularities of mean curvature flow with bounded mean curvature and Morse index Chodosh and F

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.200092Z

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Observation 6e8fa702-0d3d-447f-b21c-fcc06c216885 · outbound

This paper cites Chen and L.

Singularities of mean curvature flow with bounded mean curvature and Morse index Chen and L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.182469Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3dee8e47-7f0c-4820-bdb2-8471a4b3589d · outbound

This paper cites Ecker and G.

Singularities of mean curvature flow with bounded mean curvature and Morse index Ecker and G

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.165268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 16777106-667c-4a31-8979-26ab24817795 · outbound

This paper cites Guo and N.

Singularities of mean curvature flow with bounded mean curvature and Morse index Guo and N

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.149652Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f470b1a5-5fb0-4022-a9a5-5fcc77c2ba1c · outbound

This paper cites Haslhofer and Bruce Kleiner, Mean curvature ﬂow of me an convex hypersurfaces, Comm.

Singularities of mean curvature flow with bounded mean curvature and Morse index Haslhofer and Bruce Kleiner, Mean curvature ﬂow of me an convex hypersurfaces, Comm

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.133811Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0823fed9-3b25-4dd8-84ee-bc76223fd492 · outbound

This paper cites Huisken, Flow by mean curvature of convex surfaces into spheres, J.

Singularities of mean curvature flow with bounded mean curvature and Morse index Huisken, Flow by mean curvature of convex surfaces into spheres, J

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.116845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cac7658e-81f2-4615-9c98-900d1c5a72a7 · outbound

This paper cites Huisken, Asymptotic behavior for singularities of t he mean curvature ﬂow, J.

Singularities of mean curvature flow with bounded mean curvature and Morse index Huisken, Asymptotic behavior for singularities of t he mean curvature ﬂow, J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.100743Z

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Observation c7ac413b-36a8-4c2a-b82a-935c0fd39cab · outbound

This paper cites Huisken and C.

Singularities of mean curvature flow with bounded mean curvature and Morse index Huisken and C

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.083242Z

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Observation f80072fd-bcc3-41f5-8113-5b081a663705 · outbound

This paper cites Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature,Mem.

Singularities of mean curvature flow with bounded mean curvature and Morse index Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature,Mem

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.066963Z

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Observation 38a2328a-26d3-4995-a27f-b33055d6b459 · outbound

This paper cites Ilmanen, Lectures on mean curvature ﬂow and related e qua- tions,http://www.math.ethz.ch/ ilmanen/papers/pub.html,1995.

Singularities of mean curvature flow with bounded mean curvature and Morse index Ilmanen, Lectures on mean curvature ﬂow and related e qua- tions,http://www.math.ethz.ch/ ilmanen/papers/pub.html,1995

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.049674Z

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Observation e234eb8b-a791-40d1-9f3a-5d9e0830e956 · outbound

This paper cites Ilmanen, A strong maximum principle for singular min imal hypersurfaces, Calc.

Singularities of mean curvature flow with bounded mean curvature and Morse index Ilmanen, A strong maximum principle for singular min imal hypersurfaces, Calc

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.033477Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 69e3b923-617f-44dc-a1ae-a3d4bccca5eb · outbound

This paper cites Li and B.

Singularities of mean curvature flow with bounded mean curvature and Morse index Li and B

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:05.015842Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fbeeb434-2251-4d6e-be70-2817a1e9bc8c · outbound

This paper cites Li and B.

Singularities of mean curvature flow with bounded mean curvature and Morse index Li and B

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.999104Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 433eb200-e587-4d7d-a046-32ed7d1453fe · outbound

This paper cites Blow Up of Compact Mean Curvature Flow Solutions with Bounded Mean Curvature.

Singularities of mean curvature flow with bounded mean curvature and Morse index Blow Up of Compact Mean Curvature Flow Solutions with Bounded Mean Curvature

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-10T21:35:04.454003Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ee3a741-00ce-49dd-beb9-e74b75232675 · outbound

This paper cites Naber and D.

Singularities of mean curvature flow with bounded mean curvature and Morse index Naber and D

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.982583Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a61e0c85-ab2b-4768-8ef6-9f2f0f09a951 · outbound

This paper cites Sharp, Compactness of minimal hypersurfaces with bo unded index, J.

Singularities of mean curvature flow with bounded mean curvature and Morse index Sharp, Compactness of minimal hypersurfaces with bo unded index, J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.966313Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 366e0ca4-050e-4bcf-b194-916e2573bc53 · outbound

This paper cites Simon, Lectures on geometric measure theory, Number 3 in Proceedings of the Centre for Math- ematical Analysis, Australian National University (1984).

Singularities of mean curvature flow with bounded mean curvature and Morse index Simon, Lectures on geometric measure theory, Number 3 in Proceedings of the Centre for Math- ematical Analysis, Australian National University (1984)

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.950710Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7a3b169d-0424-472f-8d60-510719e2a31b · outbound

This paper cites Schoen and L.

Singularities of mean curvature flow with bounded mean curvature and Morse index Schoen and L

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.933910Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 69e1f157-c846-4e85-9250-2a2f0a7daf81 · outbound

This paper cites Stolarski, Existence of mean curvature ﬂow singular ities with bounded mean curvature, Duke Math.

Singularities of mean curvature flow with bounded mean curvature and Morse index Stolarski, Existence of mean curvature ﬂow singular ities with bounded mean curvature, Duke Math

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.917557Z

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Observation 3e2bfa30-b77e-44e0-942e-b939d59776ce · outbound

This paper cites On the Structure of Singularities of Weak Mean Curvature Flows with Mean Curvature Bounds.

Singularities of mean curvature flow with bounded mean curvature and Morse index On the Structure of Singularities of Weak Mean Curvature Flows with Mean Curvature Bounds

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-08-10T21:35:04.629286Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b74c5d4a-e19f-46a6-9225-d6ea717b4967 · outbound

This paper cites Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy.

Singularities of mean curvature flow with bounded mean curvature and Morse index Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-10T21:35:04.494086Z

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Unavailable: canonical work link unavailable.

Observation e98846fd-8e4a-4777-ac90-ddaf5d0a8667 · outbound

This paper cites Vel´azquez, Curvature blow-up in perturbations of minimal cones evolving by mean curvature ﬂow, Ann.

Singularities of mean curvature flow with bounded mean curvature and Morse index Vel´azquez, Curvature blow-up in perturbations of minimal cones evolving by mean curvature ﬂow, Ann

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.899581Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 03d1e15e-9ac5-4289-b19f-b81d9e866961 · outbound

This paper cites Asymptotic structure of self-shrinkers.

Singularities of mean curvature flow with bounded mean curvature and Morse index Asymptotic structure of self-shrinkers

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-08-10T21:35:04.583691Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bde7f17b-cd67-4922-9015-c82b5c82e9c6 · outbound

This paper cites White, Stratiﬁcation of minimal surfaces, mean curv ature ﬂows, and harmonic maps, J.

Singularities of mean curvature flow with bounded mean curvature and Morse index White, Stratiﬁcation of minimal surfaces, mean curv ature ﬂows, and harmonic maps, J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.881724Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ccc8f510-d660-4523-afcf-35ba96ac73c3 · outbound

This paper cites White, The size of the singular set in mean curvature ﬂ ow of mean-convex sets, J.

Singularities of mean curvature flow with bounded mean curvature and Morse index White, The size of the singular set in mean curvature ﬂ ow of mean-convex sets, J

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.865860Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f6e2f260-fc23-407f-832d-772d905bda3d · outbound

This paper cites White, The nature of singularities in mean curvature ﬂow of mean-convex sets, J.

Singularities of mean curvature flow with bounded mean curvature and Morse index White, The nature of singularities in mean curvature ﬂow of mean-convex sets, J

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.849308Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b58dbaeb-c7d3-405b-89eb-9d2b34ed1362 · outbound

This paper cites White, A local regularity theorem for mean curvature ﬂow, Ann.

Singularities of mean curvature flow with bounded mean curvature and Morse index White, A local regularity theorem for mean curvature ﬂow, Ann

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:35:04.832934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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