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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access September 2, 2017

Angles between Curves in Metric Measure Spaces

  • Bang-Xian Han and Andrea Mondino EMAIL logo

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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Received: 2017-04-13
Accepted: 2017-07-11
Published Online: 2017-09-02

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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