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Ricci-Deturck flow from rough metrics and applications

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arxiv 2204.05843 v2 pith:EP633GOP submitted 2022-04-12 math.DG

Jianchun Chu , Man-Chun Lee This is my paper · ORCID
classification math.DG
keywords applicationsflowmetricsricci-deturckroughworkbi-lipschitzconcentration
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Motivated by the recent work of Lamm and Simon, in this work we study the short-time existence theory of Ricci-Deturck flow starting from rough metrics which are bi-Lipschitz and have small local scaling invariant gradient concentration. As applications, we use it to study several stability problems related to the scalar curvature.

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  1. Preserving curvature lower bounds when Ricci flowing non-smooth initial data

    math.DG 2024-11 conditional novelty 1.0 of 10

    A survey of results on Ricci flow from non-smooth initial data, focusing on preservation of lower curvature bounds and open problems.

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