Mathematische Annalen

, Volume 353, Issue 2, pp 305-331

First online:

A rigidity theorem in Alexandrov spaces with lower curvature bound

  • Takumi YokotaAffiliated withResearch Institute for Mathematical Sciences, Kyoto University Email author 

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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.

Mathematics Subject Classification (2000)

Primary 53C23 Secondary 53C24 54E50