A canonical neighborhood theorem for the mean curvature flow in higher codimension

Abstract

In dimensions $n\ge 5$, we prove a canonical neighborhood theorem for the mean curvature flow of compact $n$-dimensional submanifolds in ${\mathbb{R}}^N$ satisfying a pinching condition $|A{|}^2<c|H{|}^2$ for $c=\min \{\frac{3(n+1)}{2n(n+2)},\frac{1}{n-2}\}.$

arXiv commentfinal version, to appear in IMRN