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

Andrews, Ben

Calc. Var. Partial Differ. Equ. 2, No. 2, 151-171 (1994).

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.

MSC:

35K55	Nonlinear parabolic equations
53A05	Surfaces in Euclidean and related spaces

Keywords:

fully nonlinear parabolic evolution equations

References:

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