# Angles between Curves in Metric Measure Spaces

Analysis and Geometry in Metric Spaces (2017)

- Volume: 5, Issue: 1, page 47-68
- ISSN: 2299-3274

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topBang-Xian Han, and Andrea Mondino. "Angles between Curves in Metric Measure Spaces." Analysis and Geometry in Metric Spaces 5.1 (2017): 47-68. <http://eudml.org/doc/288286>.

@article{Bang2017,

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.},

author = {Bang-Xian Han, Andrea Mondino},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {angle; metric measure space; Wasserstein space; curvature dimension condition; Ricci curvature},

language = {eng},

number = {1},

pages = {47-68},

title = {Angles between Curves in Metric Measure Spaces},

url = {http://eudml.org/doc/288286},

volume = {5},

year = {2017},

}

TY - JOUR

AU - Bang-Xian Han

AU - Andrea Mondino

TI - Angles between Curves in Metric Measure Spaces

JO - Analysis and Geometry in Metric Spaces

PY - 2017

VL - 5

IS - 1

SP - 47

EP - 68

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/288286

ER -

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