Optimal Transport with Branching Distance Costs and the Obstacle Problem

Abstract

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X, dN ) a possibly branching geodesic space. We show that under some assumptions on the transference plan we can reduce the transport problem to transport problems along family of geodesics. We introduce three… (More)
DOI: 10.1137/100801433

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