Contractive transport maps from $\mathbb{S}^2$ to nearly spherical surfaces with positive Ricci curvature
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918127204302848 |
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| author | Serres, Jordan |
| author_facet | Serres, Jordan |
| contents | We prove that every nearly spherical, positively curved surface is the contractive, volume-preserving image of a round sphere. The proof combines three main tools: the Ricci flow on surfaces, the Kim-Milman construction, and a multiscale Bakry-Émery criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contractive transport maps from $\mathbb{S}^2$ to nearly spherical surfaces with positive Ricci curvature Serres, Jordan Analysis of PDEs Differential Geometry Functional Analysis We prove that every nearly spherical, positively curved surface is the contractive, volume-preserving image of a round sphere. The proof combines three main tools: the Ricci flow on surfaces, the Kim-Milman construction, and a multiscale Bakry-Émery criterion. |
| title | Contractive transport maps from $\mathbb{S}^2$ to nearly spherical surfaces with positive Ricci curvature |
| topic | Analysis of PDEs Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2508.13688 |