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The Monge Problem in Geodesic Spaces

TitleThe Monge Problem in Geodesic Spaces
Publication TypeConference Paper
Year of Publication2011
AuthorsBianchini, S, Cavalletti, F
EditorBressan, A, Chen, G-QG, Lewicka, M, Wang, D
Conference NameNonlinear Conservation Laws and Applications
PublisherSpringer US
Conference LocationBoston, MA
ISBN Number978-1-4419-9554-4

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

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