Mass transportation on sub-Riemannian structures of rank two in dimension four

Abstract : 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.
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Z Badreddine. Mass transportation on sub-Riemannian structures of rank two in dimension four. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, In press. ⟨hal-01952439⟩

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