Generic regularity of Level Set Flows with spherical singularity

TL;DR

This paper characterizes the typical behavior of mean curvature flows with spherical singularities, showing that the associated arrival time function is generically at most twice differentiable.

Contribution

It provides a new characterization of the generic dynamics of MCFs with spherical singularities using level set flow formulation.

Findings

Arrival time function is generically at most C^2 regular

Sphere is the only generic compact shrinker for MCF

Characterizes the dynamics of MCFs with spherical singularity

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 $C^2$ regularity.