Angles between Curves in Metric Measure Spaces

Bang-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 -