TY - JOUR
T1 - A rigidity theorem in Alexandrov spaces with lower curvature bound
AU - Yokota, Takumi
N1 - Funding Information:
T. Yokota was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists (19.9377).
PY - 2012/6
Y1 - 2012/6
N2 - 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.
AB - 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.
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U2 - 10.1007/s00208-011-0686-8
DO - 10.1007/s00208-011-0686-8
M3 - Article
AN - SCOPUS:84860620727
SN - 0025-5831
VL - 353
SP - 305
EP - 331
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 2
ER -