Paper Citation Record · LEDGER

Liouville theorem of the subcritical biharmonic equation on complete manifolds

As of 21 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2508.14497.

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

pith.paper-citation-record.v1
2508.14497 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T18:34:57.046059Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

28 of 28 outbound references displayed

verified exact1
verified fuzzy17
unresolved10
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f8b17492-1e8a-441d-9146-fa0dff897d58 · outbound

This paper cites Beckner, Sharp Sobolev inequalities on the sphere and the Moser--Trudinger inequality, Ann.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Beckner, Sharp Sobolev inequalities on the sphere and the Moser--Trudinger inequality, Ann

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:35:01.196227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f976e82e-d401-4bd2-a2e7-2543257a819a · outbound

This paper cites Bidaut-V\'eron, L.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Bidaut-V\'eron, L

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:35:00.994914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 80dc2f4a-5118-4d6f-b66f-7618248fd353 · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:35:00.782043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 418e48bb-b478-4d96-8376-8d99213efd56 · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:35:00.588153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6a5a5346-1332-4687-b5f7-2bea45802e60 · outbound

This paper cites Case, The Obata--V\'etois argument and its applications, J.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Case, The Obata--V\'etois argument and its applications, J

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:35:00.424611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 12f23039-e4e8-46a1-beb8-3e126736fddc · outbound

This paper cites Semilinear elliptic equations on manifolds with nonnegative Ricci curvature.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Semilinear elliptic equations on manifolds with nonnegative Ricci curvature

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:34:57.185587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 832f7cbb-52b4-4d8f-a35e-6e5327d34a3a · outbound

This paper cites Catino, D.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Catino, D

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:35:00.228561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4f2f9f1c-1c37-488b-9006-f9e3160bf5e8 · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:35:00.065355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cbea26f9-4f00-41cb-9746-623635101045 · outbound

This paper cites Dolbeault, M.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Dolbeault, M

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:59.886850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1e031a18-1e17-4a7f-ac7b-d5c219195be0 · outbound

This paper cites Dolbeault, M.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Dolbeault, M

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:59.728349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f14eeb99-34cd-4e41-9283-d899e393bb68 · outbound

This paper cites Fazly, J.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Fazly, J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:59.553604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 10e25f6c-b3f7-4f03-bbeb-6f99b33c3dbe · outbound

This paper cites Fogagnolo, A.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Fogagnolo, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:59.347101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation baad24bc-8808-48bb-a7f4-1c30735e0424 · outbound

This paper cites Gidas, J.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Gidas, J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:59.189496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 43e93a19-34c9-4d61-a923-3bb2356553a9 · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:34:58.975983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 96a98fc3-98d1-4726-a954-78d53cd78f98 · outbound

This paper cites Lin, A classification of solutions of a conformally invariant fourth order equation in \( R ^n\), Comment.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Lin, A classification of solutions of a conformally invariant fourth order equation in \( R ^n\), Comment

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:58.823550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fd9c092f-8d80-40ed-b96e-c2564c57d41b · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:34:58.780449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ebb3c38b-b920-430e-b160-e73523c76fab · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:34:58.741345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1a88940b-f518-4d63-aba7-d18770a8a620 · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:34:58.606562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7afe2e15-809c-4590-b43f-e212625c9ad0 · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:34:58.457835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6338c0e6-e111-4828-a89e-bcc439bf0f7a · outbound

This paper cites Moser, A sharp form of an inequality by N.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Moser, A sharp form of an inequality by N

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:58.339630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 33da24cc-2971-4211-beb3-37f447cf9ce7 · outbound

This paper cites an unresolved cited work.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:34:58.196401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1fdadb6c-9548-4850-8598-05333d0e3625 · outbound

This paper cites Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:57.994386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 792cb2a7-2754-4958-8309-5188ff8275bb · outbound

This paper cites Obata, The conjectures on conformal transformations of Riemannian manifolds, J.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Obata, The conjectures on conformal transformations of Riemannian manifolds, J

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:57.879986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ebbfc657-10db-4303-ae7f-a519b602d927 · outbound

This paper cites Onofri, On the positivity of the effective action in a theory of random surfaces, Comm.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Onofri, On the positivity of the effective action in a theory of random surfaces, Comm

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:57.747640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3f37d1e9-13f1-49eb-998e-de4a9ac2eb8d · outbound

This paper cites Ou, On the classification of entire solutions to the critical \(p\)-Laplace equation, Math.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Ou, On the classification of entire solutions to the critical \(p\)-Laplace equation, Math

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:57.573733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 46217872-3dae-4e1a-abf8-1053f820c963 · outbound

This paper cites Critical quasilinear equations on Riemannian manifolds.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Critical quasilinear equations on Riemannian manifolds

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-05T18:34:56.897408Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12135c4f-48ac-45a8-8c80-c1b1ceebe05e · outbound

This paper cites V\'etois, Uniqueness of conformal metrics with constant Q-curvature on closed Einstein manifolds, Potential Anal.

Liouville theorem of the subcritical biharmonic equation on complete manifolds V\'etois, Uniqueness of conformal metrics with constant Q-curvature on closed Einstein manifolds, Potential Anal

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:57.453440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 672c182c-1f28-4f8c-8a18-f9655b9621fe · outbound

This paper cites Yang, Asymptotic behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities, Calc.

Liouville theorem of the subcritical biharmonic equation on complete manifolds Yang, Asymptotic behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities, Calc

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:34:57.334538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.