Optimal Transport and Generalized Ricci Flow
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866914636300812288 |
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| author | Kopfer, Eva Streets, Jeffrey |
| author_facet | Kopfer, Eva Streets, Jeffrey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01649 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal Transport and Generalized Ricci Flow Kopfer, Eva Streets, Jeffrey Differential Geometry Analysis of PDEs 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. |
| title | Optimal Transport and Generalized Ricci Flow |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2306.01649 |