Calculus of Variations and Geometric Measure Theory
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S. Bianchini - F. Cavalletti

The Monge problem in geodesic spaces

created by cavallett on 14 Jan 2011


Accepted Paper

Inserted: 14 jan 2011

Journal: ``Nonlinear Conservation Laws and Applications", IMA Vol. Math. Appl., Springer, New York.
Year: 2010


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

Keywords: optimal transportation


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