The relative volume growth of minimal submanifolds
type: Item
instance of: scholarly article
title: The relative volume growth of minimal submanifolds
zbMATH Open document ID: 1024.53042
DOI: 10.1007/BF02638388
published in: Archiv der Mathematik
publication date: 2003-03-27T00:00:00Z
review text: Let \(P^m\) be a minimal submanifold of a Riemannian manifold \(N^n\) with sectional curvatures \(K_N\) satisfying \(K_N\leq b\). Let \(D_r\) be the connected component of the intersection of \(P\) with a ball of radius \(r\) in \(N\) with center \(p\) in \(P\), with \(r\) small. Then \(D_r\) is an \(m\)-dimensional ball. This paper compares the volume of \(D_r\) with the volume of a ball of radius \(r\) in an \(m\)-dimensional space form of constant curvature \(b\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1889280
zbMATH Keywords: volume growth
zbMATH Keywords: minimal submanifold
zbMATH Keywords: sectional curvatures
zbMATH Keywords: space form
author: S. Markvorsen
author: Vicente Palmer
MaRDI profile type: Publication
Wikidata QID: Q61978221
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description: scientific article; zbMATH DE number 1889280