Existence of Mean Curvature Flow Singularities with Bounded Mean Curvature

Maxwell Stolarski

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arXiv · 2003.06383

Existence of Mean Curvature Flow Singularities with Bounded Mean Curvature

Maxwell Stolarski

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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.

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Maxwell Stolarski. 2020-03-13. Existence of Mean Curvature Flow Singularities with Bounded Mean Curvature. https://arxiv.org/abs/2003.06383

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