Mean curvature flow with surgery of mean convex surfaces in three-manifolds

Abstract

In a previous paper, we introduced a notion of mean curvature flow with surgery for embedded, mean convex surfaces in ${\mathbb{R}}^3$. In this paper, we extend this construction to embedded, mean convex surfaces in a Riemannian three-manifold. Moreover, by combining our results with earlier work of Brian White, we are able to give a precise description of the longtime behavior of the surgically modified flow.