An example of a mean-convex mean curvature flow developing infinitely many singular epochs

TL;DR

This paper presents a compact mean-convex hypersurface evolving under mean curvature flow that develops infinitely many singular epochs accumulating at zero time, illustrating complex singularity behavior.

Contribution

It provides a novel example of mean curvature flow with infinitely many singular epochs converging to zero, highlighting intricate singularity development.

Findings

Existence of a hypersurface with infinitely many singular epochs

Singular epochs accumulate at zero time

Illustrates complex singularity formation in mean curvature flow

Abstract

In this paper, we give an example of a compact mean-convex hypersurface with a single singular point moved by mean curvature having a sequence of singular epochs (times) converging to zero.