Area-minimizing regions with small volume in Riemannian manifolds with boundary
type: Item
instance of: scholarly article
title: Area-minimizing regions with small volume in Riemannian manifolds with boundary
zbMATH Open document ID: 1186.53010
author: Mouhamed Moustapha Fall
published in: Pacific Journal of Mathematics
publication date: 2010-02-23T00:00:00Z
review text: For a given domain \(\Omega\) of a Riemannian manifold, the author proves that regions minimizing the area (relative to \(\Omega\)) are nearly the maxima of the mean curvature of \(\partial \Omega\) when their volume tends to zero. He deduces some sharp local relative isoperimetric inequalities involving mean curvature comparisons.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 5673971
zbMATH Keywords: mean curvature
zbMATH Keywords: isoperimetric inequality
reviewed by: Huafei Sun
MaRDI profile type: Publication
full work available at URL: pjm.2010.244.235
OpenAlex ID: W1990257585
Wikidata QID: Q115230616
DOI: 10.2140/PJM.2010.244.235
description: scientific article; zbMATH DE number 5673971