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Contraction of convex hypersurfaces in Euclidean space. (English) Zbl 0805.35048
Summary: 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.

35K55 Nonlinear parabolic equations
53A05 Surfaces in Euclidean and related spaces
Full Text: DOI
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