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The Log Entropy Functional Along the Ricci Flow

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arxiv 0708.2008 v3 pith:UY4FRDCS submitted 2007-08-15 math.DG

Rugang Ye This is my paper · ORCID
classification math.DG
keywords alongflowriccientropyfunctionalmonotonicityconsequenceconstant
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In this paper we introduce the log entropy functional and establish its monotonicity along the Ricci flow. One consequence of it is the monotonicity of the logarithmic Sobolev constant along the Ricci flow.

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

    math.DG 2025-05 reject novelty 5.0 of 10

    The author proves W-entropy dissipation and Shannon entropy power concavity on closed (K,n,N)-super Ricci flows over metric measure spaces, and connects lower-bounded W-entropy to volume non-collapsing on RCD(0,N) spaces.

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