Generic regularity of Level Set Flows with spherical singularity

2022/04/17 by Ao Sun, Sun, Ao, Jinxin Xue +1
Mathematics · #35J70 #35K65 #37D10 #53E10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2204.07896

openalex publication_date 2022/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The sphere is well-known as the only generic compact shrinker for mean curvature flow (MCF). In this paper, we characterize the generic dynamics of MCFs with a spherical singularity. In terms of the level set flow formulation of MCF, we establish that generically the arrival time function of level set flow with spherical singularity has at most C² regularity.

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