Published Paper
Inserted: 18 jan 2017
Last Updated: 11 sep 2017
Journal: Analysis and Geometry in Metric Spaces
Volume: 5
Number: 1
Pages: 47--68
Year: 2017
Abstract:
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.
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