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articleNo Access
Optimal maps in essentially non-branching spaces
- Fabio Cavalletti and
- Andrea Mondino
Communications in Contemporary Mathematics30 Aug 2017
Preview Abstract
In this paper we prove that in a metric measure space $(X, d, 𝔪)$ verifying the measure contraction property with parameters $K \in ℝ$ and $1 < N < \infty$ , any optimal transference plan between two marginal measures is induced by an optimal map, provided the first marginal is absolutely continuous with respect to $𝔪$ and the space itself is essentially non-branching. In particular this shows that there exists a unique transport plan and it is induced by a map.

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