Non-collapsing in mean-convex mean curvature flow

2011/08/01 by Ben Andrews, Andrews, Ben
Mathematics · #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1108.0247

openalex publication_date 2011/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the interval of existence.

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