An isoembolic pinching theorem
type: Item
instance of: scholarly article
title: An isoembolic pinching theorem
zbMATH Open document ID: 0648.53025
DOI: 10.1007/BF01404458
author: Christopher B. Croke
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143572
review text: For \(\alpha\) (n) the volume of the n-sphere, Berger's isoembolic inequality states \(V/i^ n\geq \alpha (n)/\pi^ n\), where V denotes the volume, i the injectivity radius of a compact Riemannian n-manifold M. Moreover, equality holds if M is a round sphere. The author shows for an explicit constant c(n) that \[ \alpha (n)/\pi^ n+c(n)\geq V/i^ n \] implies that M is homeomorphic to \(S^ n\).
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4058344
zbMATH Keywords: isoembolic inequality
zbMATH Keywords: volume
zbMATH Keywords: injectivity radius
zbMATH Keywords: sphere
reviewed by: Werner Ballmann
MaRDI profile type: Publication
cites work: Curvature free volume estimates
cites work: On the Volume of Metric Balls
cites work: Homotopy Type Finiteness Theorems for Certain Precompact Families of Riemannian Manifolds
description: scientific article; zbMATH DE number 4058344