Mass transportation on sub-Riemannian structures of rank two in dimension four
Badreddine, Z.1, 2
1 Université Côte d'Azur, Inria, CNRS, LJAD, France
2 Université de Bourgogne, Institut de Mathématiques de Bourgogne, France
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 3, pp. 837-860.
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This paper is concerned with the study of the Monge optimal transport problem in sub-Riemannian manifolds where the cost is given by the square of the sub-Riemannian distance. Our aim is to extend previous results on existence and uniqueness of optimal transport maps to cases of sub-Riemannian structures which admit many singular minimizing geodesics. We treat here the case of sub-Riemannian structures of rank two in dimension four.

DOI : 10.1016/j.anihpc.2018.10.003
Mots-clés : Sub-Riemannian geometry, Optimal transport problem
Badreddine, Z. 1, 2

1 Université Côte d'Azur, Inria, CNRS, LJAD, France
2 Université de Bourgogne, Institut de Mathématiques de Bourgogne, France 
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Badreddine, Z. Mass transportation on sub-Riemannian structures of rank two in dimension four. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 3, pp. 837-860. doi : 10.1016/j.anihpc.2018.10.003. http://www.numdam.org/articles/10.1016/j.anihpc.2018.10.003/

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