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Monge’s transport problem in the Heisenberg group. (English) Zbl 1216.49039

Summary: We prove the existence of a solution to Monge’s transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Carathéodory distance assuming that the initial measure is absolutely continuous with respect to the Haar measure of the group.

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
53C17 Sub-Riemannian geometry
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