Contraction of convex hypersurfaces in Euclidean space
- Cite this article as:
- Andrews, B. Calc. Var (1994) 2: 151. doi:10.1007/BF01191340
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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.