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The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on RCD*(K, N) metric measure spaces. As a consequence, the new introduced notions are compatible with the corresponding classical ones for Riemannian manifolds, Ricci limit spaces and Alexandrov spaces.
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
47-68
Opis fizyczny
Daty
wydano
2017-08-28
otrzymano
2017-04-13
zaakceptowano
2017-07-11
online
2017-09-02
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Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_1515_agms-2017-0003