The Globalization Theorem for CD(K,N) on locally finite Spaces

Zhenhao Li

The Globalization Theorem for CD(K,N) on locally finite Spaces

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arxiv 2212.07962 v2 pith:TY3VLHOB submitted 2022-12-15 math.MG math.FA

Zhenhao Li This is my paper · ORCID

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keywords finitelocallyspacescavalletticonditioncurvature-dimensionessentiallyestablish

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We establish the local-to-global property of the synthetic curvature-dimension condition for essentially non-branching locally finite metric-measure spaces, extending the work [F. Cavalletti, E. Milman \textit{Invent. Math.} 226 (2021), no. 1, 1-137].

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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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