Existence of Mean Curvature Flow Singularities with Bounded Mean Curvature

Abstract

In [Vel94], Velazquez constructed a countable collection of mean curvature flow solutions in ${\mathbb{R}}^N$ in every dimension $N\ge 8$. Each of these solutions becomes singular in finite time at which time the second fundamental form blows up. In contrast, we confirm here that, in every dimension $N\ge 8$, a nontrivial subset of these solutions has uniformly bounded mean curvature.

44 pages, comments welcome