On the mean convexity of a space-and-time neighborhood of generic singularities formed by mean curvature flow

2018/03/29 by Zhou Gang, Gang, Zhou
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1803.10903

Abstract

We consider one of the generic regimes of formation of singularities. We obtain a detailed description of a possibly small, but fixed, neighborhood of the blowup point, up to (and including) the blowup time, and find that it is mean convex. This confirms a conjecture by Ilmanen. And we find that the singularity is isolated from the other ones.

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