Symmetric hypersurfaces in Riemannian manifolds contracting to Lie groups by their mean curvature
type: Item
instance of: scholarly article
title: Symmetric hypersurfaces in Riemannian manifolds contracting to Lie groups by their mean curvature
zbMATH Open document ID: 0921.53025
DOI: 10.1007/BF01189952
author: Knut Smoczyk
published in: Calculus of Variations and Partial Differential Equations
publication date: 1996-05-05T00:00:00Z
review text: Huisken proved that, under a strong convexity assumption, in Riemannian spaces a flow by mean curvature will contract a closed convex hypersurface to a point in finite time [\textit{G. Huisken}, Invent. Math. 84, 463-480 (1986; Zbl 0589.53058)]. The author generalizes the result of Huisken by showing that in a Riemannian space the flow by mean curvature of a hypersurface invariant under a subgroup of the isometry group of the ambient space will contract the hypersurface to this subgroup. This result is established under a certain technical assumption analogous to the convexity condition.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 53C45
zbMATH DE Number: 852858
zbMATH Keywords: mean curvature flow
Wikidata QID: Q115393943
reviewed by: Vladimir I. Oliker
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01189952
OpenAlex ID: W2065019872
description: scientific article; zbMATH DE number 852858