Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T14:28:44.579343Z
Paper Citation Record · LEDGER
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application
As of 19 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2505.19113.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
43 of 43 outbound references displayed
- verified exact0
- verified fuzzy28
- unresolved15
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation af96b05f-19af-47a8-9639-e11a8209812f · outbound
This paper cites Bakry, M.
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:54.845720Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8e1b1160-ae3e-45e9-b806-933994e29bde · outbound
This paper cites Bakry, Z.-M.
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:54.592167Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 2cc948b6-624c-45a1-b468-96ffdcd33a76 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:54.363592Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0d387a58-39da-42c5-a20c-791eee947bff · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:54.111120Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 58a76bec-928c-4cfb-b89a-10634b144ae5 · outbound
This paper cites Fujitani, Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds withε- range,manuscripta math., vol.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Fujitani, Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds withε- range,manuscripta math., vol
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:53.859378Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0f2158ed-f972-467a-9c02-5f5e4e620cb2 · outbound
This paper cites Fujitani, Analysis of harmonic functions under lower bounds ofN−weighted Ricci curvature with ε−range,Journal of Mathematical Analysis and Applications, vol.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Fujitani, Analysis of harmonic functions under lower bounds ofN−weighted Ricci curvature with ε−range,Journal of Mathematical Analysis and Applications, vol
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:53.672895Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ad19355e-0a1c-4f4a-a7d3-293a70fa8553 · outbound
This paper cites Grigor’yan, Heat Kernel and Analysis on Manifolds, AMS/IP Studies in Advanced Mathematics, vol.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Grigor’yan, Heat Kernel and Analysis on Manifolds, AMS/IP Studies in Advanced Mathematics, vol
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:53.451287Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 843765f7-66ba-45d9-9347-d77e08bcf6a6 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:53.197609Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d693fe9b-99df-4c0c-b30f-c8ea2f10d134 · outbound
This paper cites Hamilton, The formation of singularities in the Ricci flow, inSurveys in Differential Geometry, Vol.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Hamilton, The formation of singularities in the Ricci flow, inSurveys in Differential Geometry, Vol
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:52.926583Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9f692fb2-4a9b-42ff-864c-1db5f1dd4ade · outbound
This paper cites Karp and P.
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:52.723096Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ec258d86-c9af-4afd-aa1f-15c89972c7d4 · outbound
This paper cites Kuwae and X.-D.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Kuwae and X.-D
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:52.471333Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 514cdab4-f18b-4b37-89d3-e77d1fc61f32 · outbound
This paper cites Kuwae and Y.
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:52.254103Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation cc3c6bb0-aa61-43d1-8906-027588145197 · outbound
This paper cites Kuwae and Y.
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:52.027829Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 06b0f683-4864-4e52-96ab-3ca630cdba74 · outbound
This paper cites Kuwae and Y.
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:51.784558Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 346fbd78-34d9-4287-8269-78d644a41d82 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:51.478654Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 2b57d25e-c7b6-4033-9892-f64c185ef109 · outbound
This paper cites Li, Geometric analysis.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Li, Geometric analysis
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:51.203898Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 4f9837df-9087-4f3b-b59b-816d6b453b10 · outbound
This paper cites Li, Uniqueness ofL 1 solutions for the Laplace equation and the heat equation on Riemannian manifolds,Journal of Differential Geometry, vol.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Li, Uniqueness ofL 1 solutions for the Laplace equation and the heat equation on Riemannian manifolds,Journal of Differential Geometry, vol
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:50.924221Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c5f3f62c-7cd3-40d7-aa7d-cf4c97a8b835 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:50.687186Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8db549e6-e83a-4d43-aba0-fc457d73e351 · outbound
This paper cites Li, S.-T.
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:50.408180Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 88da2ab9-2569-457e-a3df-d742c624a44a · outbound
This paper cites Li, Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds, Journal of Mathematics Pure and Applied, vol.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Li, Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds, Journal of Mathematics Pure and Applied, vol
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:50.122027Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 086a18bc-825e-4691-b42f-59389833525b · outbound
This paper cites Li, Li-Yau-Hamilton estimates and Bakry-Émery-Ricci curvature,Nonlinear Anal.113 (2015), 1–32, Elsevier, Amsterdam.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Li, Li-Yau-Hamilton estimates and Bakry-Émery-Ricci curvature,Nonlinear Anal.113 (2015), 1–32, Elsevier, Amsterdam
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:49.896120Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ee567f3b-3643-4e01-9f48-a82fcda1fbe1 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:49.534577Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f70a1650-06e7-48e5-8420-b1983421bbb7 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:49.212364Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 4c6f992f-2427-443c-95e6-4d386a6a24c8 · outbound
This paper cites Munteanu and J.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Munteanu and J
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:48.945067Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 148837bf-dd63-45e4-89a6-7b4bbca1a959 · outbound
This paper cites Ohta,(K,N)-convexity and the curvature-dimension condition for negative N, The Journal of Geometric Analysis26, no.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Ohta,(K,N)-convexity and the curvature-dimension condition for negative N, The Journal of Geometric Analysis26, no
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:48.742503Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d2e1df53-98fb-42e9-8ac5-0a5126b98f08 · outbound
This paper cites Ohta,Comparison Finsler geometry, Springer Monographs in Mathematics, Springer, Cham, [2021] ©2021.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Ohta,Comparison Finsler geometry, Springer Monographs in Mathematics, Springer, Cham, [2021] ©2021
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:48.476426Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ad6acfb7-b078-4ab0-9a36-e83c82654b7f · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:48.261799Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a75f7247-7dd3-45d9-b37b-43c3428f2440 · outbound
This paper cites Perelmann, The entropy formula for the Ricci flow and its geometric applications.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Perelmann, The entropy formula for the Ricci flow and its geometric applications
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T14:28:42.982237Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4847ebf9-d24a-4c5e-a99f-ef3d91e26ed8 · outbound
This paper cites Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds.J.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds.J
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:47.970461Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation db03c5d3-9a6a-4671-8c59-48a5134d58c7 · outbound
This paper cites Saloff-Coste, Aspects of Sobolev-Type Inequalities.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Saloff-Coste, Aspects of Sobolev-Type Inequalities
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:47.721205Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 082d0f08-aead-4e00-b890-cb90c5f3be46 · outbound
This paper cites Sturm, On the geometry of metric measure spaces.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Sturm, On the geometry of metric measure spaces
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:47.452608Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e22e1081-6907-41f6-b220-482db18c1ec3 · outbound
This paper cites Sturm, On the geometry of metric measure spaces.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Sturm, On the geometry of metric measure spaces
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:47.187175Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a987821c-1b8a-408c-a0dc-b8a7a2882f8d · outbound
This paper cites Pigola, M.
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:46.937133Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ab3c7182-a22e-4264-90d6-8f8613e8e75f · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:46.725416Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b79c230a-994e-4ea1-a7bf-5ed3a98e78e8 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:46.491899Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 792e0bad-cb1f-4412-9d4b-ba57015d14f7 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:46.274011Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 746ca29a-bdcc-4cf5-ac70-83ea35800f37 · outbound
This paper cites Wu,L p-Liouville theorems on complete smooth metric measure spaces,”Bulletin des Sciences Mathématiques, vol.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Wu,L p-Liouville theorems on complete smooth metric measure spaces,”Bulletin des Sciences Mathématiques, vol
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:46.041793Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0c4d03b1-695c-48c5-84eb-f18fcd288551 · outbound
This paper cites Wu and P.
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:45.816548Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation fd3f4d2c-d685-4363-bed3-61c46ff81d04 · outbound
This paper cites Wu and P.
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:45.572639Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d2ee9650-a80d-4272-8c82-d082187dcd27 · outbound
This paper cites On the geometry of Riemannian manifolds with density.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application On the geometry of Riemannian manifolds with density
Reference 40
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T14:28:44.263898Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3ba35629-ea98-4b73-a903-65f09244919c · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:45.391682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 46020f38-96fe-4cb5-92a3-cc98aedb2ac3 · outbound
This paper cites Zhang, M.
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T14:28:45.175569Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 18dd68af-a0a9-4155-b5db-febdb694e747 · outbound
This paper cites an unresolved cited work.
Heat kernel estimate on weighted Riemannian manifolds under lower $N$-Ricci curvature bounds with $\epsilon$-range and it's application Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T14:28:44.981090Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Pith citing papers
No inbound Pith citation observations are available.