Contraction of convex hypersurfaces in Euclidean space

Ben Andrews

doi:10.1007/BF01191340

Contraction of convex hypersurfaces in Euclidean space

Ben Andrews^*

^*Corresponding author for this work

Mathematical Sciences Institute

Research output: Contribution to journal › Article › peer-review

218 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	151-171
Number of pages	21
Journal	Calculus of Variations and Partial Differential Equations
Volume	2
Issue number	2
DOIs	https://doi.org/10.1007/BF01191340
Publication status	Published - May 1994

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AB - 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.

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Contraction of convex hypersurfaces in Euclidean space

Abstract

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