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...
| Main Authors: | , |
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| Format: | Journal article |
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De Gruyter Open
2017
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| _version_ | 1826280393511272448 |
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| author | Han, B Mondino, A |
| author_facet | Han, B Mondino, A |
| author_sort | Han, B |
| collection | OXFORD |
| 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. |
| first_indexed | 2024-03-07T00:13:02Z |
| format | Journal article |
| id | oxford-uuid:79e6b0e3-cbba-4228-9b8c-880b9177d133 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:13:02Z |
| publishDate | 2017 |
| publisher | De Gruyter Open |
| record_format | dspace |
| spelling | oxford-uuid:79e6b0e3-cbba-4228-9b8c-880b9177d1332022-03-26T20:40:18ZAngles between curves in metric measure spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:79e6b0e3-cbba-4228-9b8c-880b9177d133Symplectic Elements at OxfordDe Gruyter Open2017Han, BMondino, AThe 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. |
| spellingShingle | Han, B Mondino, A Angles between curves in metric measure spaces |
| title | 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_short | Angles between curves in metric measure spaces |
| title_sort | angles between curves in metric measure spaces |
| work_keys_str_mv | AT hanb anglesbetweencurvesinmetricmeasurespaces AT mondinoa anglesbetweencurvesinmetricmeasurespaces |