Singularities of Mean Curvature Flow with Bounded Total Curvature

Abstract

We prove that every tangent flow at the first singular time of a smooth, closed, embedded mean curvature flow has smooth support, provided that the total curvature satisfies ${\sup }_{t\in [0,T)}{\int }_{M_t}|A{|}^{n}d{\mu }_t<\infty$. This extends Ilmanen's smoothness result for tangent flows to higher dimensions.

arXiv comment51 pages