manuscripta mathematica

, Volume 95, Issue 2, pp 225–236

Starshaped hypersurfaces¶and the mean curvature flow

  • Knut Smoczyk

DOI: 10.1007/s002290050025

Cite this article as:
Smoczyk, K. manuscripta math. (1998) 95: 225. doi:10.1007/s002290050025


Under the assumption of two a-priori bounds for the mean curvature, we are able to generalize a recent result due to Huisken and Sinestrari [8], valid for mean convex surfaces, to a much larger class. In particular we will demonstrate that these a-priori bounds are satisfied for a class of surfaces including meanconvex as well as starshaped surfaces and a variety of manifolds that are close to them. This gives a classification of the possible singularities for these surfaces in the case n= 2. In addition we prove that under certain initial conditions some of them become mean convex before the first singularity occurs.

Mathematics Subject Classification (1991): 53C42

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Knut Smoczyk
    • 1
  1. 1.Mathematics Department, ETH Zürich, HG E 18.2, CH-8092 Zürich, Switzerland.¶e-mail: ksmoczyk@math.ethz.chCH