A rigidity theorem in Alexandrov spaces with lower curvature bound

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6 Citations (Scopus)

Abstract

Distance functions of metric spaces with lower curvature bound, by definition, enjoy various metric inequalities; triangle comparison, quadruple comparison and the inequality of Lang-Schroeder-Sturm. The purpose of this paper is to study the extremal cases of these inequalities and to prove rigidity results. The spaces which we shall deal with here are Alexandrov spaces which possibly have infinite dimension and are not supposed to be locally compact.

Original languageEnglish
Pages (from-to)305-331
Number of pages27
JournalMathematische Annalen
Volume353
Issue number2
DOIs
Publication statusPublished - 2012 Jun 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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