Optimal Transport and Generalized Ricci Flow
We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton flow. This determines a formal notion of geodesics in the space of measures, and we show geodesic convexity of an associa...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212120 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Optimal Transport and Generalized Ricci Flow. Eva Kopfer and Jeffrey Streets. SIGMA 20 (2024), 003, 15 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716870605406208 |
|---|---|
| author | Kopfer, Eva Streets, Jeffrey |
| author_facet | Kopfer, Eva Streets, Jeffrey |
| citation_txt | Optimal Transport and Generalized Ricci Flow. Eva Kopfer and Jeffrey Streets. SIGMA 20 (2024), 003, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton flow. This determines a formal notion of geodesics in the space of measures, and we show geodesic convexity of an associated entropy functional. Finally, we show monotonicity of the cost along the backwards heat flow, and use this to give a new proof of the monotonicity of the energy functional along generalized Ricci flow.
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| first_indexed | 2026-03-20T15:21:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212120 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T15:21:15Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kopfer, Eva Streets, Jeffrey 2026-01-28T14:00:41Z 2024 Optimal Transport and Generalized Ricci Flow. Eva Kopfer and Jeffrey Streets. SIGMA 20 (2024), 003, 15 pages 1815-0659 2020 Mathematics Subject Classification: 53E20; 49Q22 arXiv:2306.01649 https://nasplib.isofts.kiev.ua/handle/123456789/212120 https://doi.org/10.3842/SIGMA.2024.003 We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton flow. This determines a formal notion of geodesics in the space of measures, and we show geodesic convexity of an associated entropy functional. Finally, we show monotonicity of the cost along the backwards heat flow, and use this to give a new proof of the monotonicity of the energy functional along generalized Ricci flow. We thank Micah Warren for helpful comments. The second-named author was supported by a Simons Fellowship and by the NSF via DMS-2203536. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Optimal Transport and Generalized Ricci Flow Article published earlier |
| spellingShingle | Optimal Transport and Generalized Ricci Flow Kopfer, Eva Streets, Jeffrey |
| title | Optimal Transport and Generalized Ricci Flow |
| title_full | Optimal Transport and Generalized Ricci Flow |
| title_fullStr | Optimal Transport and Generalized Ricci Flow |
| title_full_unstemmed | Optimal Transport and Generalized Ricci Flow |
| title_short | Optimal Transport and Generalized Ricci Flow |
| title_sort | optimal transport and generalized ricci flow |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212120 |
| work_keys_str_mv | AT kopfereva optimaltransportandgeneralizedricciflow AT streetsjeffrey optimaltransportandgeneralizedricciflow |