Paper Citation Record · LEDGER

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds

As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:1908.03697.

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

pith.paper-citation-record.v1
1908.03697 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:31:47.269689Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

21 of 21 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e2ea50b5-7e05-4a5c-b9be-76c0483ace17 · outbound

This paper cites an unresolved cited work.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:31:47.627130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 051de9e5-0f0c-45db-b72f-fd6adb71cdb1 · outbound

This paper cites Ambrosio, X.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Ambrosio, X

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.612106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 495b8e87-f743-4ea6-8000-48f361a52f20 · outbound

This paper cites Calabi, An extension of E.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Calabi, An extension of E

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.597220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 86c07b9d-6bc4-4d84-ad47-4cafb8086a37 · outbound

This paper cites an unresolved cited work.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:31:47.582090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5e2fcbd6-f65c-4fdb-9a40-c13ac28ad1ac · outbound

This paper cites an unresolved cited work.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:31:47.566294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 10a1cc5a-2993-46f9-97ab-0e965d348a96 · outbound

This paper cites De Giorgi, Convergence problems for functionals and operato rs, In Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rom e, 1978), pages 131-.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds De Giorgi, Convergence problems for functionals and operato rs, In Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rom e, 1978), pages 131-

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.549643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 42ca111a-3cf1-473d-abd3-bd51c05f0790 · outbound

This paper cites del Pino, M.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds del Pino, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.518468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 02d999f4-5a9c-41e4-8062-9bd65d2c1d2b · outbound

This paper cites Ghoussoub, C.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Ghoussoub, C

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.503099Z

Source-reported events for the cited work

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Observation 52e7e823-4a45-4883-8ba3-4f690ae89dda · outbound

This paper cites an unresolved cited work.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:31:47.488426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0a93ae17-a2e8-486f-be4b-0d04483c06d3 · outbound

This paper cites Ma, Gradient estimates for a simple elliptic equation on non-com pact Riemannian mani- folds, J.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Ma, Gradient estimates for a simple elliptic equation on non-com pact Riemannian mani- folds, J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.473517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8259625f-a7f2-47b8-93f5-b5293d9d9655 · outbound

This paper cites an unresolved cited work.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:31:47.458200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 65ebbb0c-9d2c-4708-8bba-8671fc1131a0 · outbound

This paper cites Modica, A gradient bound and a liouville theorem for nonlinear po isson equations, Com- mun.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Modica, A gradient bound and a liouville theorem for nonlinear po isson equations, Com- mun

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.442239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f5ac4003-22e7-4cce-8421-4de47adf0859 · outbound

This paper cites Negrin, Gradient estimates and a Liouville type theorem for th e Schr¨ odinger operator, J.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Negrin, Gradient estimates and a Liouville type theorem for th e Schr¨ odinger operator, J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.426225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fad2d1ad-fb88-4cb9-bc8c-4d45b16d27ed · outbound

This paper cites Pacard, M.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Pacard, M

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.411000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e39d21b7-ad49-4056-b566-25382ee77390 · outbound

This paper cites Ratto, M.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Ratto, M

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.393766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a283456c-cae7-4d33-8f42-d740531ab63f · outbound

This paper cites an unresolved cited work.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:31:47.375486Z

Source-reported events for the cited work

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Observation a337d666-9256-433f-9799-a4da219ec9df · outbound

This paper cites Souplet, Q.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Souplet, Q

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.358937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 26153986-cfb1-45eb-b4ab-7423c7abb81a · outbound

This paper cites Yang, Gradient estimates for a nonlinear parabolic equation o n Riemannian manifolds, Proc.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Yang, Gradient estimates for a nonlinear parabolic equation o n Riemannian manifolds, Proc

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.341676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 31460e77-f77e-4e56-af2d-d1ed1637ba9c · outbound

This paper cites Yang, Gradient estimates for the equation ∆ u + cu− α = 0 on Riemannian manifolds, Acta Math.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Yang, Gradient estimates for the equation ∆ u + cu− α = 0 on Riemannian manifolds, Acta Math

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:31:47.325047Z

Source-reported events for the cited work

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Observation 760c1219-d4c0-4cb8-8c94-bc118c799d1b · outbound

This paper cites an unresolved cited work.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:31:47.307999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 00a90651-bc05-4216-a700-1a0fbfc1aea0 · outbound

This paper cites an unresolved cited work.

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds Unresolved cited work

Reference 188

Resolution: parse uncertain; raw_fallback, observed 2026-08-14T14:31:47.533720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

No inbound Pith citation observations are available.