On mean curvature flow with driving force starting as singular initial hypersurface

TL;DR

This paper investigates the evolution of axisymmetric hypersurfaces under mean curvature flow with a driving force, focusing on singular initial conditions and using level set methods to determine fattening behavior.

Contribution

It provides criteria to distinguish between fattening and non-fattening interface evolutions in mean curvature flow with singular initial hypersurfaces.

Findings

Criteria for fattening vs. non-fattening evolution

Analysis of singular initial hypersurfaces

Application of level set method to this problem

Abstract

We consider an axisymmetric closed hypersurface evolving by its mean curvature with driving force under singular initial hypersurface. We study this problem by level set method. We give some criteria to judge whether the interface evolution is fattening or non-fattening.