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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.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Takumi Yokota

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  1. Takumi Yokota
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Correspondence to Takumi Yokota.

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

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Yokota, T. A rigidity theorem in Alexandrov spaces with lower curvature bound. Math. Ann. 353, 305–331 (2012). https://doi.org/10.1007/s00208-011-0686-8

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  • DOI: https://doi.org/10.1007/s00208-011-0686-8

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