Rotational symmetry of solutions of mean curvature flow coming out of a double cone

TL;DR

This paper proves that solutions to the mean curvature flow originating from a rotationally symmetric double cone preserve rotational symmetry throughout their evolution.

Contribution

It establishes that rotational symmetry is maintained for smooth solutions of mean curvature flow starting from a symmetric double cone.

Findings

Solutions remain rotationally symmetric during evolution

Symmetry preservation holds for smooth solutions

Provides insight into symmetry behavior in geometric flows

Abstract

We show that any smooth solution to the mean curvature flow equations coming out of a rotationally symmetric double cone is also rotationally symmetric.