Abstract
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 $c = \min \{ \frac {3(n+1)}{2n(n+2)},\frac {1}{n-2}\}.$
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