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

  • Simon Brendle

    Columbia University, New York, USA
  • Gerhard Huisken

    Universität Tübingen, Germany

Abstract

In a previous paper, we introduced a notion of mean curvature flow with surgery for embedded, mean convex surfaces in . 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.

Cite this article

Simon Brendle, Gerhard Huisken, Mean curvature flow with surgery of mean convex surfaces in three-manifolds. J. Eur. Math. Soc. 20 (2018), no. 9, pp. 2239–2257

DOI 10.4171/JEMS/811