Isometries in Aleksandrov spaces of curvature bounded above
type: Item
instance of: scholarly article
title: Isometries in Aleksandrov spaces of curvature bounded above
zbMATH Open document ID: 1027.53040
published in: Illinois Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: By studying isometries of Aleksandrov spaces of curvature bounded above by a negative number, the author proves the following theorem: if \(M\) is a locally compact complete and geodesically complete \(\Re_{K}\)-domain (or \(\text{CAT}( K) \)-space), \(K<0\), in which all spheres are arcwise connected, then every bijection \(f\) of the space \(M\) onto itself such that \(f\) and \(f^{-1}\) map any closed ball of some fixed radius \(r>0\) onto some closed ball of radius \(r\), is an isometry. For hyperbolic spaces, a stronger result by \textit{A. V. Kuz'minykh} [Sib. Mat. Zh. 20, 597-602 (1979; Zbl 0427.51008)] is known.
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 53C45
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1839967
zbMATH Keywords: isometry
zbMATH Keywords: CAT(k)-space
zbMATH Keywords: hyperbolic spaces
zbMATH Keywords: spheres
zbMATH Keywords: Alexandrov spaces
author: V. N. Berestovskij
reviewed by: Igor G. Nikolaev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1839967