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Uniquely minimizing costs for the Kantorovitch problem
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 3, pp. 507-563.

L’objet de cet article est de mettre en évidence des conditions suffisantes pertinentes et efficaces qui garantissent l’unicité des solutions aux problème de Kantorovitch et de démontrer la densité des coûts continus sur une variété pour lesquels les plans de transport optimaux sont uniques. Nous proposons également un critère pratique pour l’unicité des solutions au problème de Kantorovitch dans le cadre d’espaces polonais non-compacts.

The purpose of the present paper is to establish comprehensive and systematic sufficient conditions for uniqueness of the Kantorovitch optimizer, and to prove the density of continuous costs on arbitrary manifolds for which optimal plans are unique. We shall also establish a practical criterion for the uniqueness of the Kantorovitch optimizer in the non-compact setting on Polish spaces.

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DOI : https://doi.org/10.5802/afst.1638
@article{AFST_2020_6_29_3_507_0,
     author = {Abbas Moameni and Ludovic Rifford},
     title = {Uniquely minimizing costs for the Kantorovitch problem},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {507--563},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {3},
     year = {2020},
     doi = {10.5802/afst.1638},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1638/}
}
Abbas Moameni; Ludovic Rifford. Uniquely minimizing costs for the Kantorovitch problem. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 3, pp. 507-563. doi : 10.5802/afst.1638. https://afst.centre-mersenne.org/articles/10.5802/afst.1638/

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