Contraction of convex hypersurfaces in Euclidean space

  • Ben Andrews

DOI: 10.1007/BF01191340

Cite this article as:
Andrews, B. Calc. Var (1994) 2: 151. doi:10.1007/BF01191340


We consider a class of fully nonlinear parabolic evolution equations for hypersurfaces in Euclidean space. A new geometrical lemma is used to prove that any strictly convex compact initial hypersurface contracts to a point in finite time, becoming spherical in shape as the limit is approached. In the particular case of the mean curvature flow this provides a simple new proof of a theorem of Huisken.

Mathematics subject classification

35K55 53A05 

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Ben Andrews
    • 1
  1. 1.Centre for Mathematics and its ApplicationsAustralian National UniversityCanberraAustralia