manuscripta mathematica

, Volume 95, Issue 1, pp 225–236 | Cite as

Starshaped hypersurfaces and the mean curvature flow

  • Knut Smoczyk


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 casen=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)



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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Knut Smoczyk
    • 1
  1. 1.Mathematics DepartmentETH Zürich, HG E 18.2ZürichSwitzerland

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