{"ID":2889704,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.20959","arxiv_id":"2507.20959","title":"Benamou-Brenier and Kantorovich on sub-Riemannian manifolds with no abnormal geodesics","abstract":"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.","short_abstract":"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 $2$-momentu...","url_abs":"https://arxiv.org/abs/2507.20959","url_pdf":"https://arxiv.org/pdf/2507.20959v2","authors":"[\"Giovanna Citti\",\"Mattia Galeotti\",\"Andrea Pinamonti\"]","published":"2025-07-28T16:10:33Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}