Angles between Curves in Metric Measure Spaces

• Autorzy: Bang-Xian Han , Andrea Mondino
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

angle; metric measure space; Wasserstein space; curvature dimension condition; Ricci curvature

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 47-68

Daty

wydano

2017-08-28

otrzymano

2017-04-13

zaakceptowano

2017-07-11

online

2017-09-02

Twórcy

autor

Bang-Xian Han

• ,

autor

Andrea Mondino

• ,

Identyfikatory

DOI

10.1515/agms-2017-0003