Paper Citation Record · LEDGER

A sharp isoperimetric inequality and the top order $Q$-curvature

As of 11 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 2 inbound Pith citation observations for arXiv:2607.06951.

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

pith.paper-citation-record.v1
2607.06951 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-09T22:42:51.044093Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T15:54:27.304751Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

45 of 45 outbound references displayed

verified exact3
verified fuzzy37
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 72d975ff-302f-4462-93d8-82ca9ca1e029 · outbound

This paper cites Agostiniani, M.

A sharp isoperimetric inequality and the top order $Q$-curvature Agostiniani, M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:35.999154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1499cd08-ae5e-417a-a083-309d15be59be · outbound

This paper cites Balogh, A.

A sharp isoperimetric inequality and the top order $Q$-curvature Balogh, A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.048323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 76bd6be9-eb54-4fde-9128-12e40d071081 · outbound

This paper cites Beckenbach, T.

A sharp isoperimetric inequality and the top order $Q$-curvature Beckenbach, T

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.002684Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4fd0f8a9-bcc6-4dc4-84dd-ecc89c80447d · outbound

This paper cites Benjamini, J.

A sharp isoperimetric inequality and the top order $Q$-curvature Benjamini, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.044488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d7ef2910-5296-41d1-9ade-aa970616fa03 · outbound

This paper cites Besse, Einstein manifolds, Ergeb.

A sharp isoperimetric inequality and the top order $Q$-curvature Besse, Einstein manifolds, Ergeb

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.052089Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a91c5f43-7397-45e8-b564-ad6b8949befb · outbound

This paper cites ISBN:3-540-15279-2.

A sharp isoperimetric inequality and the top order $Q$-curvature ISBN:3-540-15279-2

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.038818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b5b93d5c-1516-4627-82c5-bd4be9d12769 · outbound

This paper cites an unresolved cited work.

A sharp isoperimetric inequality and the top order $Q$-curvature Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-07-09T22:46:36.004696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9d921e49-df7a-438a-aa00-4b5d92e1d984 · outbound

This paper cites Brendle, Sobolev inequalities in manifolds with nonnegative curvature, Comm.

A sharp isoperimetric inequality and the top order $Q$-curvature Brendle, Sobolev inequalities in manifolds with nonnegative curvature, Comm

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.061729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation af1a9c83-8e69-4249-95fd-2f0250ae9fa7 · outbound

This paper cites Bol, Isoperimetrische Ungleichungen f¨ ur Bereiche auf Fl¨ achen, Jber.

A sharp isoperimetric inequality and the top order $Q$-curvature Bol, Isoperimetrische Ungleichungen f¨ ur Bereiche auf Fl¨ achen, Jber

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.046411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8f42785f-0816-4edc-b5a8-9d2b818fe0a5 · outbound

This paper cites Caffarelli, L.

A sharp isoperimetric inequality and the top order $Q$-curvature Caffarelli, L

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.017867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 82ed53dc-20df-4b50-a6e1-98cae064daf4 · outbound

This paper cites Cavalletti, A.

A sharp isoperimetric inequality and the top order $Q$-curvature Cavalletti, A

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.057699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b5d498b6-31e0-457d-a414-46db1b68526e · outbound

This paper cites Chang, M.

A sharp isoperimetric inequality and the top order $Q$-curvature Chang, M

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.047249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f28336f5-fb32-479c-ba55-17d7ed68634b · outbound

This paper cites Chang, J.

A sharp isoperimetric inequality and the top order $Q$-curvature Chang, J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.064154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3d5fd5b3-8536-4488-a66b-3aa05244d1f0 · outbound

This paper cites Cohn-Vossen, K¨ urzeste Wege und Totalkr¨ ummung auf Fl¨ achen, Compositio Math.

A sharp isoperimetric inequality and the top order $Q$-curvature Cohn-Vossen, K¨ urzeste Wege und Totalkr¨ ummung auf Fl¨ achen, Compositio Math

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.030603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ccd98f2a-3102-4ded-a169-613a618e68d7 · outbound

This paper cites Croke, A sharp four-dimensional isoperimetric inequality, Comment.

A sharp isoperimetric inequality and the top order $Q$-curvature Croke, A sharp four-dimensional isoperimetric inequality, Comment

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.036485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b6c4123b-a173-4a4b-941d-3757aa438792 · outbound

This paper cites David, S.

A sharp isoperimetric inequality and the top order $Q$-curvature David, S

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.029430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e15d5cdd-1148-4bb9-a12d-7345587ec25a · outbound

This paper cites Fang, On a conformal Gauss–Bonnet–Chern inequality for LCF manifolds and related topics, Calc.

A sharp isoperimetric inequality and the top order $Q$-curvature Fang, On a conformal Gauss–Bonnet–Chern inequality for LCF manifolds and related topics, Calc

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.025848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e4ac472a-b783-47b9-8e8e-87499747615f · outbound

This paper cites Fefferman, C.R.

A sharp isoperimetric inequality and the top order $Q$-curvature Fefferman, C.R

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.056069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 05829401-7449-4aad-a8be-50c50ae0ee55 · outbound

This paper cites Fiala, Le probl` eme des isop´ erim` etres sur les surfaces ouvertes ` a courbure positive, Comment.

A sharp isoperimetric inequality and the top order $Q$-curvature Fiala, Le probl` eme des isop´ erim` etres sur les surfaces ouvertes ` a courbure positive, Comment

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.008534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d78c1875-a199-45af-af54-774cf281c8e6 · outbound

This paper cites Finn, On a class of conformal metrics, with application to differential geometry in the large, Comment.

A sharp isoperimetric inequality and the top order $Q$-curvature Finn, On a class of conformal metrics, with application to differential geometry in the large, Comment

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.001118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0c546a2c-84a2-4b83-b9e8-7f9ca3c0c8f1 · outbound

This paper cites Ghomi, J.

A sharp isoperimetric inequality and the top order $Q$-curvature Ghomi, J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.054204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1eb3c171-268f-4d0f-9a9b-9ec4e9278c9f · outbound

This paper cites an unresolved cited work.

A sharp isoperimetric inequality and the top order $Q$-curvature Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-07-09T22:46:36.032748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 00323b5e-ae7e-4a2a-8834-56377e22769a · outbound

This paper cites Hartman, Geodesic parallel coordinates in the large.

A sharp isoperimetric inequality and the top order $Q$-curvature Hartman, Geodesic parallel coordinates in the large

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.050841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5cde65df-a8f0-4476-9037-a64fccbdefb6 · outbound

This paper cites Huber, On the isoperimetric inequality on surfaces of variable Gaussian curvature, Ann.

A sharp isoperimetric inequality and the top order $Q$-curvature Huber, On the isoperimetric inequality on surfaces of variable Gaussian curvature, Ann

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.061891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation febbac54-d69a-457e-a5e1-876bdfa3d5cc · outbound

This paper cites Huber, On subharmonic functions and differential geometry in the large, Comment.

A sharp isoperimetric inequality and the top order $Q$-curvature Huber, On subharmonic functions and differential geometry in the large, Comment

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.068737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 39a6bdfc-ac52-4935-9efe-cb07629f525e · outbound

This paper cites Kleiner, An isoperimetric comparison theorem, Invent.

A sharp isoperimetric inequality and the top order $Q$-curvature Kleiner, An isoperimetric comparison theorem, Invent

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.031163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f1848d1a-9802-4786-8d6f-ed6747328fe7 · outbound

This paper cites Li, The total Q-curvature, volume entropy and polynomial growth polyharmonic functions, Adv.

A sharp isoperimetric inequality and the top order $Q$-curvature Li, The total Q-curvature, volume entropy and polynomial growth polyharmonic functions, Adv

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.057868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 58669fbd-6ff0-40be-b9d4-79783e9b0c63 · outbound

This paper cites Conformal metrics with finite total Q-curvature revisited.

A sharp isoperimetric inequality and the top order $Q$-curvature Conformal metrics with finite total Q-curvature revisited

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-07-09T22:46:35.912493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 265dfa91-3a8b-4cbf-99cf-34aede9ecb15 · outbound

This paper cites an unresolved cited work.

A sharp isoperimetric inequality and the top order $Q$-curvature Unresolved cited work

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-07-09T22:46:35.909891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 47b365ed-308b-4334-b8ed-4e057b89f1af · outbound

This paper cites an unresolved cited work.

A sharp isoperimetric inequality and the top order $Q$-curvature Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-07-09T22:46:36.042558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c05f2dce-e108-4d68-9411-0859e465d40e · outbound

This paper cites Li, L.-F.

A sharp isoperimetric inequality and the top order $Q$-curvature Li, L.-F

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.021805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d9a9c39c-9180-4a1b-ba91-0ec1369a3765 · outbound

This paper cites Ma, Cohn-Vossen theory for locally conformally flat manifolds, arXiv:2606.13979.

A sharp isoperimetric inequality and the top order $Q$-curvature Ma, Cohn-Vossen theory for locally conformally flat manifolds, arXiv:2606.13979

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-09T22:46:35.916430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1853af9c-d5e1-4eb6-96ce-371ff55768e3 · outbound

This paper cites an unresolved cited work.

A sharp isoperimetric inequality and the top order $Q$-curvature Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-07-09T22:46:36.039983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e5693f74-a7d5-4b1a-b131-41bdf05c8023 · outbound

This paper cites Ndiaye, J.

A sharp isoperimetric inequality and the top order $Q$-curvature Ndiaye, J

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.066378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8a5d0e91-0d1d-4d2c-9d2a-293120da38a7 · outbound

This paper cites Osserman, The isoperimetric inequality, Bull.

A sharp isoperimetric inequality and the top order $Q$-curvature Osserman, The isoperimetric inequality, Bull

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.016046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4be2bd46-dad2-4c5f-a760-8c4f50636715 · outbound

This paper cites Peterson, Future directions of research in geometry: A summary of the panel dis- cussion at the 2007 Midwest Geometry Conference, SIGMA Symmetry Integrability Geom.

A sharp isoperimetric inequality and the top order $Q$-curvature Peterson, Future directions of research in geometry: A summary of the panel dis- cussion at the 2007 Midwest Geometry Conference, SIGMA Symmetry Integrability Geom

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.059446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7f76a267-6bf2-4389-8d31-5db814eacc20 · outbound

This paper cites Schulze, Nonlinear evolution by mean curvature and isoperimetric inequalities, J.

A sharp isoperimetric inequality and the top order $Q$-curvature Schulze, Nonlinear evolution by mean curvature and isoperimetric inequalities, J

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.034635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ad36d6f2-4f24-426a-87d8-8c8321eec187 · outbound

This paper cites Semmes, Bi-Lipschitz mappings and strongA ∞ weights, Ann.

A sharp isoperimetric inequality and the top order $Q$-curvature Semmes, Bi-Lipschitz mappings and strongA ∞ weights, Ann

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.055933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation dee2ce72-287c-4be0-9da3-04f310206587 · outbound

This paper cites Shiohama, Total curvatures and minimal areas of complete surfaces.

A sharp isoperimetric inequality and the top order $Q$-curvature Shiohama, Total curvatures and minimal areas of complete surfaces

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:35.988152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 002755b8-cee2-47bc-93bc-d9991a9ae1a2 · outbound

This paper cites an unresolved cited work.

A sharp isoperimetric inequality and the top order $Q$-curvature Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-07-09T22:46:36.052561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1701959d-19c3-494a-ad59-502eeeb6d568 · outbound

This paper cites Topping, Mean curvature flow and geometric inequalities, J.

A sharp isoperimetric inequality and the top order $Q$-curvature Topping, Mean curvature flow and geometric inequalities, J

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.053987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d356b9ad-dc01-407d-a94d-4207cee224c7 · outbound

This paper cites Wang, The isoperimetric inequality and quasiconformal maps on manifolds with finite total Q-curvature, Int.

A sharp isoperimetric inequality and the top order $Q$-curvature Wang, The isoperimetric inequality and quasiconformal maps on manifolds with finite total Q-curvature, Int

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.050145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 002cb62b-d8d3-4a36-93fa-fabd677776c4 · outbound

This paper cites Wang, The isoperimetric inequality and Q-curvature, Adv.

A sharp isoperimetric inequality and the top order $Q$-curvature Wang, The isoperimetric inequality and Q-curvature, Adv

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.048956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8ac26146-708a-4bb9-b231-700c605eff03 · outbound

This paper cites Weil, Sur les surfaces a courbure negative, C.R.

A sharp isoperimetric inequality and the top order $Q$-curvature Weil, Sur les surfaces a courbure negative, C.R

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.043685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4e2ccd04-321b-41c0-804c-f93ebbe7974f · outbound

This paper cites Xiao, Toward best isoperimetric constants for (H 1, BM O)-normal conformal met- rics onR n,n≥3, Adv.

A sharp isoperimetric inequality and the top order $Q$-curvature Xiao, Toward best isoperimetric constants for (H 1, BM O)-normal conformal met- rics onR n,n≥3, Adv

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-07-09T22:46:36.038243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 81428b8d-d5b8-479c-9659-87dd0c39f035 · inbound

Positivity and non-positivity results for the sixth-order $Q$-curvature of conformal metrics in $\mathbb{R}^n$ cites this paper.

Positivity and non-positivity results for the sixth-order $Q$-curvature of conformal metrics in $\mathbb{R}^n$ A sharp isoperimetric inequality and the top order $Q$-curvature

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T15:54:27.304751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7767e30-fa39-45de-b4c9-0fb93c6ec1d8 · inbound

Bonnet-Myers type theorems for $Q$-curvature on four-manifolds cites this paper.

Bonnet-Myers type theorems for $Q$-curvature on four-manifolds A sharp isoperimetric inequality and the top order $Q$-curvature

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T02:56:09.666167Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.