Benamou-Brenier and Kantorovich on sub-Riemannian manifolds with no abnormal geodesics
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| Format: | Preprint |
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2025
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| _version_ | 1866912649461104640 |
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| author | Citti, Giovanna Galeotti, Mattia Pinamonti, Andrea |
| author_facet | Citti, Giovanna Galeotti, Mattia Pinamonti, Andrea |
| contents | We prove that the Benamou-Brenier formulation of the Optimal Transport problem and the Kantorovich formulation are equivalent on a sub-Riemannian connected and complete manifold $M$ without boundary and with no non-trivial abnormal geodesics, when the problems are considered between two measures with finite $2$-momentum. Furthermore, we prove the existence of a minimizer for the Benamou-Brenier formulation and link it to the optimal transport plan. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_20959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Benamou-Brenier and Kantorovich on sub-Riemannian manifolds with no abnormal geodesics Citti, Giovanna Galeotti, Mattia Pinamonti, Andrea Optimization and Control 49Q22, 53C17 We prove that the Benamou-Brenier formulation of the Optimal Transport problem and the Kantorovich formulation are equivalent on a sub-Riemannian connected and complete manifold $M$ without boundary and with no non-trivial abnormal geodesics, when the problems are considered between two measures with finite $2$-momentum. Furthermore, we prove the existence of a minimizer for the Benamou-Brenier formulation and link it to the optimal transport plan. |
| title | Benamou-Brenier and Kantorovich on sub-Riemannian manifolds with no abnormal geodesics |
| topic | Optimization and Control 49Q22, 53C17 |
| url | https://arxiv.org/abs/2507.20959 |