RIGOT, Séverine - Analyse Harmonique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex

Abstract :

We give a solution of the optimal transport problem in groups of type H when the cost function is the square of either the Carnot-Carathéodory or Korányi distance. We prove in both cases existence, uniqueness and give a characterization of the optimal transport map. In the case of the Carnot-Carathéodory distance we also prove that the optimal transport is the limit of the optimal transports in natural Riemannian approximations, introducing in particular so-called cc-exponential coordinates in the group that may be recovered through the limit of the usual Riemannian exponential maps in the approximating Riemannian manifolds. This extends results already known for the Heisenberg groups.

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Contact : Severine.Rigot@math.u-psud.fr