Paper Citation Record · LEDGER

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator

As of 9 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2505.22439.

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

pith.paper-citation-record.v1
2505.22439 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:24:08.522918Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

27 of 27 outbound references displayed

verified exact1
verified fuzzy10
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2a7803fc-2d76-402a-ad3c-536ff8da51e0 · outbound

This paper cites Alikakos and Giorgio Fusco, The spectrum of the Cahn-Hilliard operator for generic interface in higher space dimensions, Indiana Univ.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Alikakos and Giorgio Fusco, The spectrum of the Cahn-Hilliard operator for generic interface in higher space dimensions, Indiana Univ

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:13.618437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0cf7f2f5-b9f9-44ea-a4bb-d8ca7843d441 · outbound

This paper cites 211 (2013), no.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator 211 (2013), no

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:13.313755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b0790820-97ef-4354-822e-3ba017c6a7d6 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:13.012072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 78169afe-fbb3-4434-8d7e-d401ee9339ec · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:12.882334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b7cfb19f-0ea3-4a21-8947-eb105050b6ed · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:12.744256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 35574318-28f0-4b00-9d85-98fd6bb88ce7 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:12.599993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bea06fd7-d188-4445-9a4a-ef29e6543470 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:12.443743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 54e065d5-21e0-4cee-9fc2-dc8a54e211de · outbound

This paper cites Harrell, II and Michael Loss, On the Laplace operator penalized by mean curvature, Comm.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Harrell, II and Michael Loss, On the Laplace operator penalized by mean curvature, Comm

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:12.227946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 34c8edc5-9b24-468b-abd0-c903a302d706 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:11.997629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 501afe34-3614-46ab-84be-8aeb981189d0 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:11.826500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6e98d0bd-b509-41a0-bbdc-ffe2cc2a706c · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:11.566166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 35a5c960-8ff4-46f0-9dce-e56b27c52608 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:11.201208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 959f912d-90e2-4833-801e-6b0d2e2546bd · outbound

This paper cites Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:24:08.647011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 47ae4d33-377b-48bb-bcc1-9fa5ba3db4e3 · outbound

This paper cites Differential Geom.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Differential Geom

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:10.997335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e54189c1-8c3d-410a-9f4d-8ac684e12c27 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:10.795207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 80386821-6b2d-461d-a987-f0db8dac2532 · outbound

This paper cites Blaine Lawson, Jr., Complete minimal surfaces in S3, Ann.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Blaine Lawson, Jr., Complete minimal surfaces in S3, Ann

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:10.542141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 595727a6-4968-4f60-a3bc-e39e8a95414c · outbound

This paper cites Lee, Introduction to Riemannian manifolds, 2nd edition ed., Grad.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Lee, Introduction to Riemannian manifolds, 2nd edition ed., Grad

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:10.380402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 62633534-f744-418f-a163-47e7b5b45ee1 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:10.214086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 41a1336c-da9f-4e61-aed5-3787b9d116a1 · outbound

This paper cites Manzano, Julia Plehnert, and Francisco Torralbo, Compact embedded minimal surfaces in S2 × S1, Comm.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Manzano, Julia Plehnert, and Francisco Torralbo, Compact embedded minimal surfaces in S2 × S1, Comm

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:09.986483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8ae92322-0ed6-4290-8e28-0365ed40f191 · outbound

This paper cites Marques and Andr´ e Neves,Min-max theory and the Willmore conjecture, Ann.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Marques and Andr´ e Neves,Min-max theory and the Willmore conjecture, Ann

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:09.764278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ff391b60-18a0-4cb5-bdb6-83ea059660e3 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:09.568847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8552d050-cae5-4880-a9eb-bd9b999d5c86 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:09.412937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 718f940f-8fa0-4e56-89a9-4d05ab146bb1 · outbound

This paper cites Nadirashvili, Berger’s isoperimetric problem and minimal immersions of surfaces, Geom.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Nadirashvili, Berger’s isoperimetric problem and minimal immersions of surfaces, Geom

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:09.310472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a18a079b-4c03-483b-94d4-2a882a3cf173 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:09.202968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 98bc9ad1-aebd-48ff-a561-ab79da3f87bb · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:09.066120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7d93f99c-c890-4b54-b62d-ac9741043a11 · outbound

This paper cites an unresolved cited work.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:24:08.949609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ce4aba27-5ebe-41da-b021-464f5c91b8ae · outbound

This paper cites Yang and Shing Tung Yau, Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, Ann.

Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator Yang and Shing Tung Yau, Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, Ann

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:24:08.813730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

No inbound Pith citation observations are available.