| Title | The Monge Problem in Geodesic Spaces |
| Publication Type | Conference Paper |
| Year of Publication | 2011 |
| Authors | Bianchini, S, Cavalletti, F |
| Editor | Bressan, A, Chen, G-QG, Lewicka, M, Wang, D |
| Conference Name | Nonlinear Conservation Laws and Applications |
| Publisher | Springer US |
| Conference Location | Boston, MA |
| ISBN Number | 978-1-4419-9554-4 |
| Abstract | 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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