2009/12/01 by Takumi Yokota, Yokota, Takumi
Mathematics · #53C23 (primary) #53C24 #54E50 (secondary) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG #msc:53C23 #msc:53C24 #msc:54E50
paper · pdf · doi:10.48550/arxiv.0912.0114
23 pages
arxiv created 2009/12/01 · openalex publication_date 2009/12/01 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.