Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below

Published 25 May 2021 in math.DG, math.FA, and math.MG | (2105.12017v1)

Abstract: In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of a transport map between two suitable marginals and the so-called local-to-global property.

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