A radius sphere theorem
type: Item
instance of: scholarly article
title: A radius sphere theorem
zbMATH Open document ID: 0801.53029
DOI: 10.1007/BF01232447
author: Karsten Grove
author: Peter Petersen
published in: Inventiones Mathematicae
publication date: 1994-04-12T00:00:00Z
full work available at URL: https://eudml.org/doc/144114
review text: There is a generalization of the diameter sphere theorem due to \textit{K. Grove} and \textit{K. Shiohama} [Ann. Math. (2) 106, 201--211 (1977; Zbl 0357.53027)] to the case of Alexandrov spaces due to Perelman: An \(n\)-dimensional Alexandrov space with curvature \(\geq 1\) and diameter \(> \pi/2\) is a suspension. The main result of this paper is the following sphere theorem: An \(n\)-dimensional Alexandrov space \(M\) with curvature \(\geq 1\) and radius \(>\pi/2\) is homeomorphic to the \(n\)-sphere. Here the radius is given by \(\min_{p \in M} \max_{q \in M}\text{dist}(p,q)\).
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 549673
zbMATH Keywords: sphere theorem
zbMATH Keywords: diameter
zbMATH Keywords: Alexandrov space
zbMATH Keywords: curvature
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
cites work: An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures
cites work: Q3747347
cites work: A generalization of Berger's rigidity theorem for positively curved manifolds
cites work: The low-dimensional metric foliations of Euclidean spheres
cites work: Filling Riemannian manifolds
cites work: New Extremal Problems for the Riemannian Recognition Program via Alexandrov Geometry
cites work: Volume comparison à la Aleksandrov
cites work: Hard and soft packing radius theorems
cites work: The topological spherical space form problem. II: Existence of free actions
cites work: A new version of differentiable sphere theorem
cites work: Spaces of Wald curvature bounded below
cites work: Q3473766
cites work: Q5522742
cites work: Q3270939
cites work: Q4695266
description: scientific article; zbMATH DE number 549673