Paper Citation Record · LEDGER

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below

As of 11 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2607.04588.

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

pith.paper-citation-record.v1
2607.04588 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T16:49:00.826488Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+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

18 of 18 outbound references displayed

verified exact0
verified fuzzy0
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 24fbbfa6-84e6-4522-987f-8fa79258b94a · outbound

This paper cites Bakry, M.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Bakry, M

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47ada956-7c09-4c69-88cc-ff4262612ca8 · outbound

This paper cites Barta, Sur la vibration fundamentale d’une membrane , C.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Barta, Sur la vibration fundamentale d’une membrane , C

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5545cd62-58dd-47cd-b8c9-0e871b06dce7 · outbound

This paper cites Chavel, Eigenvalues in Riemannian Geometry , Academic Press, New York (1984).

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Chavel, Eigenvalues in Riemannian Geometry , Academic Press, New York (1984)

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f33e96aa-9937-4d4f-9758-0ab02dde1d63 · outbound

This paper cites an unresolved cited work.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42617de9-fc77-40b7-9761-bbfd9e48ee34 · outbound

This paper cites On the Ashbaugh-Benguria type conjecture about lower-order Neumann eigenvalues of the Witten-Laplacian.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below On the Ashbaugh-Benguria type conjecture about lower-order Neumann eigenvalues of the Witten-Laplacian

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76753922-938d-4381-8a6b-5038b6385d7d · outbound

This paper cites an unresolved cited work.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2bcf788-7e7f-45a1-8311-caa3c7499547 · outbound

This paper cites an unresolved cited work.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2113e60e-e6ad-4fb8-8c11-d90b8996c50d · outbound

This paper cites an unresolved cited work.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed6fcb04-1e24-4d58-8f93-4bb32e4421b4 · outbound

This paper cites an unresolved cited work.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c6e9b3fe-6022-41e2-9ed1-9e03d8e5fed0 · outbound

This paper cites an unresolved cited work.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b026901d-f87b-49c0-a72f-b0af6dc2fe3f · outbound

This paper cites Freitas, J.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Freitas, J

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9dfb3591-dc3b-4fef-a707-db8b9ef366b7 · outbound

This paper cites Mao, Eigenvalue estimation and some results on ﬁnite topologica l type, Ph.D.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Mao, Eigenvalue estimation and some results on ﬁnite topologica l type, Ph.D

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db138aca-fc79-431e-b88b-b44e8710c879 · outbound

This paper cites Mao, Eigenvalue inequalities for the p-Laplacian on a Riemannian manifold and estimates for the heat kernel , J.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Mao, Eigenvalue inequalities for the p-Laplacian on a Riemannian manifold and estimates for the heat kernel , J

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 77cce047-89ac-463a-9d7f-a6409dabff2b · outbound

This paper cites Mao, The Gagliardo-Nirenberg inequalities and manifolds with n on-negative weighted Ricci curvature , Kyushu J.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Mao, The Gagliardo-Nirenberg inequalities and manifolds with n on-negative weighted Ricci curvature , Kyushu J

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24b0b3c3-df9a-4091-94d6-a0c0c8719ed1 · outbound

This paper cites Mao, Functional inequalities and manifolds with nonnegative we ighted Ricci curva- ture, Czech.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Mao, Functional inequalities and manifolds with nonnegative we ighted Ricci curva- ture, Czech

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f0fa844-b61f-44d2-ab81-5b50c899d615 · outbound

This paper cites Mao, Weighted heat kernel comparison theorems and its applicati ons in spectral geometry, submitted and available online at arXiv:2603.00942v2.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Mao, Weighted heat kernel comparison theorems and its applicati ons in spectral geometry, submitted and available online at arXiv:2603.00942v2

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 164e0f7c-d717-40d9-8c4c-f8cadf1fea14 · outbound

This paper cites an unresolved cited work.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06b3bcea-f440-4484-9d91-f737d5f64cfd · outbound

This paper cites an unresolved cited work.

Eigenvalue comparison theorems for the Witten-Laplacian and the weighted $p$-Laplacian on complete manifolds with a modified Ricci curvature bounded from below Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T16:49:00.826488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.