Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
type: Item
instance of: scholarly article
title: Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
zbMATH Open document ID: 0589.53058
DOI: 10.1007/BF01388742
author: Gerhard Huisken
published in: Inventiones Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143347
review text: The author generalizes results he obtained earlier [cf. J. Differ. Geom. 20, 237-266 (1984; Zbl 0556.53001)]. A closed ''sufficiently convex'' hypersurface of a Riemannian manifold N can be shrunk by its mean curvature to a small sphere and to a point. ''Sufficiently convex'' is specified by a lower bound for the principal curvatures depending on the curvature of N and its derivative.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 3947125
zbMATH Keywords: parabolic system
zbMATH Keywords: convex hypersurface
zbMATH Keywords: evolution equation
zbMATH Keywords: mean curvature
Wikidata QID: Q115393640
reviewed by: Dirk Ferus
MaRDI profile type: Publication
cites work: Three-manifolds with positive Ricci curvature
cites work: Sobolev and isoperimetric inequalities for riemannian submanifolds
cites work: Flow by mean curvature of convex surfaces into spheres
cites work: Q5533735
cites work: Curvature estimates for minimal hypersurfaces
cites work: Minimal varieties in Riemannian manifolds
cites work: Transformation Groups and Natural Bundles
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description: scientific article; zbMATH DE number 3947125