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

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 $\mathrm{\mid }A{\mathrm{\mid }}^2<c\mathrm{\mid }H{\mathrm{\mid }}^2$ for $c = \min { \frac{3(n+1)}{2n(n+2)},\frac{1}{n-2}}.$