Paper Citation Record · LEDGER

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary

As of 18 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2412.21008.

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

pith.paper-citation-record.v1
2412.21008 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:17:17.922449Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-29T05:27:47.034437Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-29T15:13:32.251321Z

Reference resolution

38 of 38 outbound references displayed

verified exact2
verified fuzzy22
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fbc58544-59fa-4bcb-9133-1e1dbc692ce9 · outbound

This paper cites an unresolved cited work.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:17:18.361015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation cc9883eb-9956-4001-9d52-4264c7fa3cd3 · outbound

This paper cites A note on the isoperimetric constant.Ann.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary A note on the isoperimetric constant.Ann

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T23:17:17.784205Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a30c8a54-8adb-40da-94f7-05471353c7b8 · outbound

This paper cites Geometry and spectra of compact Riemann surfaces.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Geometry and spectra of compact Riemann surfaces

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-10T23:17:17.788068Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 250f7cb2-1b1a-4d11-80f2-c7e7090540bd · outbound

This paper cites Isoperimetric control of the Steklov spectrum.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Isoperimetric control of the Steklov spectrum

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.337036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8ff3b4b0-40fe-40f1-aca4-7ec504eb60fa · outbound

This paper cites Some recent develop- ments on the Steklov eigenvalue problem.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Some recent develop- ments on the Steklov eigenvalue problem

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.326259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 334df1c0-28e3-43fa-b938-c5f39f42b2c9 · outbound

This paper cites The Steklov spectrum and coarse discretizations of manifolds with boundary.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary The Steklov spectrum and coarse discretizations of manifolds with boundary

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.315133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2c1cafa3-1a36-47fb-9a48-eabbbf48e752 · outbound

This paper cites Sharp Steklov upper bound for submanifolds of revolution.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Sharp Steklov upper bound for submanifolds of revolution

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.304909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4e62414f-62aa-43c7-98c2-3cbca4ce72e7 · outbound

This paper cites an unresolved cited work.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:17:18.293808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8f569b6f-a249-43a7-9155-b056c6b85898 · outbound

This paper cites an unresolved cited work.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:17:18.282817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7ef06c2f-2bdd-48f7-be2a-06930cca64c1 · outbound

This paper cites an unresolved cited work.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:17:18.271239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0e6b556a-75ed-48da-8ab5-f8b5cd6f41e6 · outbound

This paper cites The first Steklov eigenvalue, conformal geometry, and minimal surfaces.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary The first Steklov eigenvalue, conformal geometry, and minimal surfaces

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.260319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f964d059-4bcf-4b2b-90b4-41bd0b0a8c42 · outbound

This paper cites Shape optimization for the Steklov problem in higher dimensions.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Shape optimization for the Steklov problem in higher dimensions

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.248528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e5f899cb-9527-4a44-b1d2-b8221b27d261 · outbound

This paper cites Upper bounds for Steklov eigenvalues on surfaces.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Upper bounds for Steklov eigenvalues on surfaces

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.235923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7160a054-3b55-4061-9c0a-84bba450381e · outbound

This paper cites Spectral geometry of the Steklov problem (survey article).

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Spectral geometry of the Steklov problem (survey article)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.225153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8547405e-be56-4c04-9974-871513c0f3b7 · outbound

This paper cites Large Steklov eigenvalues on hyperbolic surfaces.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Large Steklov eigenvalues on hyperbolic surfaces

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.213540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2be2d00c-7c04-4b23-8ca4-995f87e92ddb · outbound

This paper cites Higher order Cheeger inequalities for Steklov eigen- values.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Higher order Cheeger inequalities for Steklov eigen- values

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.201840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2c062c12-6f45-406a-9146-0c4a1ded4e23 · outbound

This paper cites Non-simple systoles on random hyperbolic surfaces for large genus, 2023.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Non-simple systoles on random hyperbolic surfaces for large genus, 2023

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.190894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c9f84346-ba21-4971-a63a-a6d4e967ef83 · outbound

This paper cites Upper bounds for the Steklov eigenvalues on trees.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Upper bounds for the Steklov eigenvalues on trees

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T23:17:17.846371Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 541f31c7-e0b1-485e-9a02-45afeb2f394c · outbound

This paper cites First eigenvalue estimates of Dirichlet-to-Neumann operators on graphs.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary First eigenvalue estimates of Dirichlet-to-Neumann operators on graphs

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T23:17:17.850053Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c527039-8d3f-4e72-a52c-b6b84541de0e · outbound

This paper cites Cheeger type inequalities associated with isocapacitary constants on graphs.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Cheeger type inequalities associated with isocapacitary constants on graphs

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:17:17.987593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f4cd077b-9cca-4303-a0f4-27ef122fbb69 · outbound

This paper cites Une in´ egalit´ e de Cheeger pour le spectre de Steklov.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Une in´ egalit´ e de Cheeger pour le spectre de Steklov

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.165816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation eb134059-2832-4045-871e-3ad5d2eac6db · outbound

This paper cites Variational aspects of Laplace eigenvalues on Riemannian surfaces.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Variational aspects of Laplace eigenvalues on Riemannian surfaces

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.153980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7a00d2fc-5689-4405-9b9e-4917b7b6249e · outbound

This paper cites The legacy of Vladimir Andreevich Steklov.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary The legacy of Vladimir Andreevich Steklov

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.142520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 85d18fb1-2a37-4902-a70a-ea6ac236e13d · outbound

This paper cites Geometric analysis , volume 134 of Cambridge Studies in Advanced Mathematics.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Geometric analysis , volume 134 of Cambridge Studies in Advanced Mathematics

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-10T23:17:17.869676Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb341036-9ca9-4e95-ab08-61642875c5b3 · outbound

This paper cites an unresolved cited work.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:17:18.123115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1fb1830b-d4bb-456c-ad58-95dc2093dbca · outbound

This paper cites an unresolved cited work.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:17:18.111965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9ecc674a-7a23-473d-b0a1-792e79a0e325 · outbound

This paper cites Conductor and capacitary inequalities for functions on topological spaces and their applications to Sobolev-type imbeddings.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Conductor and capacitary inequalities for functions on topological spaces and their applications to Sobolev-type imbeddings

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.101002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 903dbc14-1a8c-4bcb-9077-352465def75a · outbound

This paper cites Integral and isocapacitary inequalities.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Integral and isocapacitary inequalities

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.089442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 44cc22a0-9afb-42e8-bf96-69fda6b8b9db · outbound

This paper cites an unresolved cited work.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:17:18.077947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9705787d-003c-4db2-b9d2-65143c385d88 · outbound

This paper cites Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-10T23:17:17.893079Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ede393af-4e83-4d3e-975d-518e65a2e106 · outbound

This paper cites Lower bounds for the first eigenvalue of the Steklov problem on graphs.Calc.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Lower bounds for the first eigenvalue of the Steklov problem on graphs.Calc

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.059897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 10acf404-54c0-422e-b074-21e2844a5576 · outbound

This paper cites Isoperimetric upper bound for the first eigenvalue of discrete Steklov problems.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Isoperimetric upper bound for the first eigenvalue of discrete Steklov problems

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.047708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a68f2d7e-d1b6-4ff1-8d86-ad200fa0678f · outbound

This paper cites Methods of modern mathematical physics.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Methods of modern mathematical physics

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.035769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 19e28b93-9b8c-4ee9-ba35-2ee606bdb00d · outbound

This paper cites Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-10T23:17:17.906998Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eeee572d-dc81-4003-aac8-f61719241489 · outbound

This paper cites A Lichnerowicz-type estimate for Steklov eigenvalues on graphs and its rigidity.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary A Lichnerowicz-type estimate for Steklov eigenvalues on graphs and its rigidity

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.024171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation fea39ae3-c19f-4df2-a17b-46e3b0ca82c9 · outbound

This paper cites Inequalities for a classical eigenvalue problem.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Inequalities for a classical eigenvalue problem

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:18.010881Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a02b6d51-7bb5-496d-819b-63a8f6136700 · outbound

This paper cites Prime geodesic theorem and closed geodesics for large genus.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Prime geodesic theorem and closed geodesics for large genus

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:17:17.959912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 3367d195-64b6-435b-b75e-698f8732ed4c · outbound

This paper cites Random hyperbolic surfaces of large genus have first eigenvalues greater than 3 16 − ϵ.

Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary Random hyperbolic surfaces of large genus have first eigenvalues greater than 3 16 − ϵ

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:17:17.998869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation 859d1cf3-c954-4a98-82cc-b421c1270468 · inbound

Lower bounds for the low Steklov eigenvalues cites this paper.

Lower bounds for the low Steklov eigenvalues Cheeger type inequalities associated with isocapacitary constants on Riemannian manifolds with boundary

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-06-29T15:13:32.253086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.