Stability of optimal transport maps on Riemannian manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913818923237376 |
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| author | Kitagawa, Jun Letrouit, Cyril Mérigot, Quentin |
| author_facet | Kitagawa, Jun Letrouit, Cyril Mérigot, Quentin |
| contents | We prove quantitative bounds on the stability of optimal transport maps and Kantorovich potentials from a fixed source measure $ρ$ under variations of the target measure $μ$, when the cost function is the squared Riemannian distance on a Riemannian manifold. Previous works were restricted to subsets of Euclidean spaces, or made specific assumptions either on the manifold, or on the regularity of the transport maps. Our proof techniques combine entropy-regularized optimal transport with spectral and integral-geometric techniques. As some of the arguments do not rely on the Riemannian structure, our work also paves the way towards understanding stability of optimal transport in more general geometric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of optimal transport maps on Riemannian manifolds Kitagawa, Jun Letrouit, Cyril Mérigot, Quentin Metric Geometry Optimization and Control 49Q22, 49K40, 53C65 We prove quantitative bounds on the stability of optimal transport maps and Kantorovich potentials from a fixed source measure $ρ$ under variations of the target measure $μ$, when the cost function is the squared Riemannian distance on a Riemannian manifold. Previous works were restricted to subsets of Euclidean spaces, or made specific assumptions either on the manifold, or on the regularity of the transport maps. Our proof techniques combine entropy-regularized optimal transport with spectral and integral-geometric techniques. As some of the arguments do not rely on the Riemannian structure, our work also paves the way towards understanding stability of optimal transport in more general geometric spaces. |
| title | Stability of optimal transport maps on Riemannian manifolds |
| topic | Metric Geometry Optimization and Control 49Q22, 49K40, 53C65 |
| url | https://arxiv.org/abs/2504.05412 |