A note on the isoperimetric dimension of a manifold
type: Item
instance of: scholarly article
title: A note on the isoperimetric dimension of a manifold
zbMATH Open document ID: 0991.53019
author: Alina Stancu
published in: Expositiones Mathematicae
publication date: 2002-08-29T00:00:00Z
review text: Using the notion of the isoperimetric dimension introduced by M. Gromov the author gives another proof for a result of \textit{R. Hamilton} [Commun. Anal. Geom. 2, 167-172 (1994; Zbl 0843.53002)]: Let \(M\) be a smooth strictly convex complete hypersurface bounding a region in Euclidean space. Suppose that its second fundamental form is \(\varepsilon\)-pinched. Then \(M\) is compact. This may be used to prove Huisken's result on compact convex hypersurfaces shrinking under the mean curvature flow.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1453276
zbMATH Keywords: isoperimetric inequality
zbMATH Keywords: isoperimetric dimension
zbMATH Keywords: convex hypersurface
zbMATH Keywords: pinched second fundamental form
reviewed by: Eberhard Teufel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453276