Weak scalar curvature lower bounds along Ricci flow

2021/10/23 by Jiang, Wenshuai, Sheng, Weimin, Zhang, Huaiyu · 1 citation
#53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.12157

Abstract

In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon that the Ricci flow exists for a short time. We prove that the scalar curvature lower bound is preserved along the Ricci flow if the initial metric has a scalar curvature lower bound in distributional sense provided that the initial metric is W^1,p for some n

Cited by

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

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