A Generalization of Caffarelli's Contraction Theorem to Nearly Spherical Manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909937814208512 |
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| author | Ge, Yuxin Serres, Jordan |
| author_facet | Ge, Yuxin Serres, Jordan |
| contents | We show that every nearly spherical manifold can be realized as the volume-preserving image of a round sphere, via the Brenier-McCann optimal transport map. This theorem extends Caffarelli's contraction theorem to nearly spherical manifolds and yields, as a corollary, a proof of a perturbative form of Milman's conjecture. The proof is based on a novel stability result for optimal transport maps on the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalization of Caffarelli's Contraction Theorem to Nearly Spherical Manifolds Ge, Yuxin Serres, Jordan Analysis of PDEs Differential Geometry Functional Analysis Probability We show that every nearly spherical manifold can be realized as the volume-preserving image of a round sphere, via the Brenier-McCann optimal transport map. This theorem extends Caffarelli's contraction theorem to nearly spherical manifolds and yields, as a corollary, a proof of a perturbative form of Milman's conjecture. The proof is based on a novel stability result for optimal transport maps on the sphere. |
| title | A Generalization of Caffarelli's Contraction Theorem to Nearly Spherical Manifolds |
| topic | Analysis of PDEs Differential Geometry Functional Analysis Probability |
| url | https://arxiv.org/abs/2512.01496 |