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

Abstract

In dimensions $n \geq 5$, 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 $c = \min \{ \frac{3(n+1)}{2n(n+2)},\frac{1}{n-2}\}.$