## Existence and uniqueness of optimal transport maps

#### Martin HuesmannRheinische Friedrich-Wilhelms-Universität Bonn

Let $(X,d,m)$ be a non-branching Polish metric measure space. We show existence and uniqueness of optimal transport maps for cost written as non-decreasing and strictly convex functions of the distance, provided the space satisfies the measure contraction property. (This is joint work with Fabio Cavalletti.)

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