, Volume 353, Issue 2, pp 305-331
Date: 17 Jun 2011

A rigidity theorem in Alexandrov spaces with lower curvature bound

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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.

T. Yokota was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists (19.9377).