A planarity estimate for pinched solutions of mean curvature flow

Abstract

We show that the blow-ups of compact solutions to the mean curvature flow in ${\mathbb{R}}^N$ initially satisfying the pinching condition $|A{|}^2<c|H{|}^2$ for a suitable constant $c=c(n)$ must be codimension one.

title changed, final version, accepted to Duke Math J