Mean curvature flow with surgery

Abstract

We give a new proof for the existence of mean curvature flow with surgery of $2$-convex hypersurfaces in ${\mathbb{R}}^N$. Our proof works for all $N\ge 3$, including mean convex surfaces in ${\mathbb{R}}^3$. We also derive a priori estimates for a more general class of flows in a local and flexible setting.