Ricci flow of W^2,2-metrics in four dimensions

2021/09/17 by Tobias Lamm, Lamm, Tobias, Miles Simon +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2109.08541

openalex publication_date 2021/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct solutions to Ricci DeTurck flow in four dimensions on closed manifolds which are instantaneously smooth but whose initial values g are (possibly) non-smooth Riemannian metrics whose components in smooth coordinates belong to W^2,2 and satisfy (1)/(a)h≤ g≤ a h for some 1

Cited by

• Ricci-DeTurck flow of almost continuous L²-metrics, and metrics with distributional scalar curvature bounded from below

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