Stability of optimal transport on metric measure spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912950399270912 |
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| author | Han, Bang-Xian Zhu, Zhuo-Nan |
| author_facet | Han, Bang-Xian Zhu, Zhuo-Nan |
| contents | We prove a quantitative stability of Kantorovich potentials on metric measure spaces with lower Ricci curvature bound, thereby confirming a recent conjecture of Kitagawa, Letrouit and Mérigot. Our proof, which employs the heat kernel-regularized $c$-transform, does not rely on linear structure or sectional curvature bounds. As a corollary, we get a quantitative stability of optimal transport maps on Alexandrov spaces with lower curvature bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19175 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability of optimal transport on metric measure spaces Han, Bang-Xian Zhu, Zhuo-Nan Metric Geometry Analysis of PDEs 53C23, 51F99, 49Q22 We prove a quantitative stability of Kantorovich potentials on metric measure spaces with lower Ricci curvature bound, thereby confirming a recent conjecture of Kitagawa, Letrouit and Mérigot. Our proof, which employs the heat kernel-regularized $c$-transform, does not rely on linear structure or sectional curvature bounds. As a corollary, we get a quantitative stability of optimal transport maps on Alexandrov spaces with lower curvature bound. |
| title | Stability of optimal transport on metric measure spaces |
| topic | Metric Geometry Analysis of PDEs 53C23, 51F99, 49Q22 |
| url | https://arxiv.org/abs/2602.19175 |