The Monge Problem for Distance Cost in Geodesic Spaces

@inproceedings{Bianchini2010TheMP,
  title={The Monge Problem for Distance Cost in Geodesic Spaces},
  author={Stefano Bianchini},
  year={2010}
}
We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dL is a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each… CONTINUE READING

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