Paper Citation Record · LEDGER

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces

As of 23 August 2026, this Paper Citation Record lists 61 of 61 outbound references and 1 inbound Pith citation observation for arXiv:2505.03202.

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

pith.paper-citation-record.v1
2505.03202 v1

Coverage vector

measured 61 of 61 reference resolution

Typed states for the displayed outbound observations.

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

61 of 61 outbound references displayed

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Outbound references

Observation a50b0fb5-bb22-4355-bd37-bf0d5f63bc39 · outbound

This paper cites an unresolved cited work.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 1

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Observation 53dbe0ef-dce5-48f0-ab42-b7227ff4db9e · outbound

This paper cites Duke Math.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Duke Math

Reference 2

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Observation c074e834-18b8-4681-bfe6-fbefa03f2eb1 · outbound

This paper cites S´ eminaire de probabilit´ es, XIX, 1983/1984.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces S´ eminaire de probabilit´ es, XIX, 1983/1984

Reference 3

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 4

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 5

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Observation bcc8a1cb-c721-4c3d-bcce-dae255b32b40 · outbound

This paper cites Perelman's entropy and heat kernel bounds on RCD spaces.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Perelman's entropy and heat kernel bounds on RCD spaces

Reference 6

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 7

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 8

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This paper cites Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows

Reference 9

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 10

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Observation 002ea708-9e2b-4cf0-95fc-ab59edbbc5c4 · outbound

This paper cites S.-T.: A lower bound for the heat kernel.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces S.-T.: A lower bound for the heat kernel

Reference 11

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Observation 21f8854c-fd50-44ca-913f-b43109c180c5 · outbound

This paper cites B., Lu, P., Ni, L.: Hamilton’s Ricci Flow, Lectures in Comtempo rary Maths., Sciences Press, Beijing, Amer.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces B., Lu, P., Ni, L.: Hamilton’s Ricci Flow, Lectures in Comtempo rary Maths., Sciences Press, Beijing, Amer

Reference 12

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Observation 654c93d0-8174-4c32-9ae0-10f86570d548 · outbound

This paper cites The Globalization Theorem for the Curvature Dimension Condition.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces The Globalization Theorem for the Curvature Dimension Condition

Reference 13

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This paper cites IEEE Trans.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces IEEE Trans

Reference 14

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 15

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Observation f5a43929-f7bf-44f5-bd59-0ef7bc3b1842 · outbound

This paper cites Cambridge Unive rsity Press, Cambridge (1990).

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Cambridge Unive rsity Press, Cambridge (1990)

Reference 16

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 17

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Observation 0750e965-579a-4686-a39a-a70cec096ca9 · outbound

This paper cites De Gruyter Studies in Mathematics.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces De Gruyter Studies in Mathematics

Reference 18

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 19

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 20

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Observation ea0b9fd4-9e11-4682-8ed1-1440f074a3af · outbound

This paper cites Hamilton, The formation of singularities in the Ricci ﬂow, Surv eys in Diﬀerential Geometry, 2, 7-136, International Press, 1995.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Hamilton, The formation of singularities in the Ricci ﬂow, Surv eys in Diﬀerential Geometry, 2, 7-136, International Press, 1995

Reference 21

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This paper cites Discrete Contin.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Discrete Contin

Reference 22

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 23

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 24

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 25

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Kleiner, J

Reference 26

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Manuscripta Math

Reference 27

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Pure and Appl

Reference 29

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Paciﬁc J

Reference 30

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 32

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Observation 1615d88c-4618-4006-be16-9c83b7ad2fe8 · outbound

This paper cites On the Renyi entropy power and the Gagliardo-Nirenberg-Sobolev inequality on Riemannian manifolds.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces On the Renyi entropy power and the Gagliardo-Nirenberg-Sobolev inequality on Riemannian manifolds

Reference 33

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces 61 (2018), 1 385-1406

Reference 34

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces 49 (2019), no

Reference 35

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 36

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Tohoku Math

Reference 37

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 38

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This paper cites Li, Perelman’s W-entropy for the Fokker-Planck equation over complete Riemannian man- ifolds, Bull.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Li, Perelman’s W-entropy for the Fokker-Planck equation over complete Riemannian man- ifolds, Bull

Reference 39

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 40

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This paper cites Li.: Sobolev inequalities on forms and Lp,q - cohomology on complete Riemannian manifolds, J Geom Anal (2010) 20: 354-387 DOI 10.1007/s12220-009-9114- 7.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Li.: Sobolev inequalities on forms and Lp,q - cohomology on complete Riemannian manifolds, J Geom Anal (2010) 20: 354-387 DOI 10.1007/s12220-009-9114- 7

Reference 41

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 42

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 43

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Observation 180849f7-f6eb-4b9f-bdd4-0cec1bb6cf5a · outbound

This paper cites The Globalization Theorem for CD(K,N) on locally finite Spaces.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces The Globalization Theorem for CD(K,N) on locally finite Spaces

Reference 44

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 45

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This paper cites On the $W$-entropy and Shannon entropy power on RCD$(K, N)$ and RCD$(K, n, N)$ spaces.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces On the $W$-entropy and Shannon entropy power on RCD$(K, N)$ and RCD$(K, n, N)$ spaces

Reference 46

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 47

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 48

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 49

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 50

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Observation 207007f2-9e20-42f1-a89c-497c9dfc2810 · outbound

This paper cites , http://arXiv.org/abs/maths0211159.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces , http://arXiv.org/abs/maths0211159

Reference 51

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Observation 2d5f362f-c365-472e-a556-93d7a284186a · outbound

This paper cites The entropy formula for linear equation.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces The entropy formula for linear equation

Reference 52

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Observation de49e59f-fac4-4a69-a4fa-249c0b0de313 · outbound

This paper cites Bell Sys tem Tech.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Bell Sys tem Tech

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:03:44.077451Z

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Observation 0e90311e-a6e5-4917-b631-a7ad03cec38a · outbound

This paper cites an unresolved cited work.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 54

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:03:44.178748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ad712272-e916-4b72-8f8a-cb7ff9abf025 · outbound

This paper cites an unresolved cited work.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 55

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5fb0ab54-9f9d-48c6-aa56-a3889ab986d1 · outbound

This paper cites Acta Math.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Acta Math

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:03:44.000817Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2dc53b28-81fc-4825-b994-711df328b25f · outbound

This paper cites Nonlinear Anal.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Nonlinear Anal

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:03:43.593553Z

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Observation a2d91a6e-e24d-423e-99fd-1499681b3ce1 · outbound

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:03:43.762482Z

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Observation 65d9f3df-9739-4a4a-a1ab-985314d9dc34 · outbound

This paper cites an unresolved cited work.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:03:43.437149Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2ac92fae-ccab-435b-bef9-523d40cb80a1 · outbound

This paper cites The Log Entropy Functional Along the Ricci Flow.

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces The Log Entropy Functional Along the Ricci Flow

Reference 60

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Observation 09a50f45-ff48-4469-a003-b5bbcfce2274 · outbound

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On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces Unresolved cited work

Reference 2008

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:03:45.563903Z

Source-reported events for the cited work

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Pith citing papers

Observation 2bc1cec9-8a45-460f-acd2-38d345e011b2 · inbound

On weak formulations of (super) Ricci flows cites this paper.

On weak formulations of (super) Ricci flows On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces

Reference 17

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.