Geodesic
Angles between Curves in Metric Measure Spaces
Analysis and Geometry in Metric Spaces, Tome 5 (2017) no. 1, pp. 47-68
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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.
Mots-clés : angle, metric measure space, Wasserstein space, curvature dimension condition, Ricci curvature 
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     title = {Angles between {Curves} in {Metric} {Measure} {Spaces}},
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     url = {http://geodesic.mathdoc.fr/item/AGMS_2017_5_1_a2/}
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Han, Bang-Xian; Mondino, Andrea. Angles between Curves in Metric Measure Spaces. Analysis and Geometry in Metric Spaces, Tome 5 (2017) no. 1, pp. 47-68. http://geodesic.mathdoc.fr/item/AGMS_2017_5_1_a2/