Absolute Continuity of Wasserstein Geodesics in the Heisenberg Group
نویسندگان
چکیده
In this paper we answer to a question raised by Ambrosio and Rigot [2] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is absolutely continuous if one of the end-points is. Since our proof relies on the validity of the so-called Measure Contraction Property and on the fact that the optimal transport map exists and the Wasserstein geodesic is unique, the absolute continuity of Wasserstein geodesic also holds for Alexandrov spaces with curvature bounded from below.
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