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Angles between Curves in Metric Measure Spaces

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Han B.-X., Mondino A.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

47-68

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.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Han B.-X.

1 Mondino A.

1 2017

Wyniki wyszukiwania

Angles between Curves in Metric Measure Spaces