Angles between Curves in Metric Measure Spaces

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...

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Autores principales:	Han Bang-Xian, Mondino Andrea
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	angle metric measure space wasserstein space curvature dimension condition ricci curvature Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/2a349efd4afa4b19acc4c60caf1cdbe9
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id	oai:doaj.org-article:2a349efd4afa4b19acc4c60caf1cdbe9
record_format	dspace
spelling	oai:doaj.org-article:2a349efd4afa4b19acc4c60caf1cdbe92021-12-05T14:10:38ZAngles between Curves in Metric Measure Spaces2299-327410.1515/agms-2017-0003https://doaj.org/article/2a349efd4afa4b19acc4c60caf1cdbe92017-09-01T00:00:00Zhttps://doi.org/10.1515/agms-2017-0003https://doaj.org/toc/2299-3274The 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.Han Bang-XianMondino AndreaDe Gruyterarticleanglemetric measure spacewasserstein spacecurvature dimension conditionricci curvatureAnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 5, Iss 1, Pp 47-68 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	angle metric measure space wasserstein space curvature dimension condition ricci curvature Analysis QA299.6-433
spellingShingle	angle metric measure space wasserstein space curvature dimension condition ricci curvature Analysis QA299.6-433 Han Bang-Xian Mondino Andrea Angles between Curves in Metric Measure Spaces
description	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.
format	article
author	Han Bang-Xian Mondino Andrea
author_facet	Han Bang-Xian Mondino Andrea
author_sort	Han Bang-Xian
title	Angles between Curves in Metric Measure Spaces
title_short	Angles between Curves in Metric Measure Spaces
title_full	Angles between Curves in Metric Measure Spaces
title_fullStr	Angles between Curves in Metric Measure Spaces
title_full_unstemmed	Angles between Curves in Metric Measure Spaces
title_sort	angles between curves in metric measure spaces
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/2a349efd4afa4b19acc4c60caf1cdbe9
work_keys_str_mv	AT hanbangxian anglesbetweencurvesinmetricmeasurespaces AT mondinoandrea anglesbetweencurvesinmetricmeasurespaces
_version_	1718371887723053056

Angles between Curves in Metric Measure Spaces

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