On the Kähler Geometry of Certain Optimal Transport Problems
Gabriel Khan,
Jun Zhang
Abstract:Let X and Y be domains of R n equipped with probability measures µ and ν, respectively. We consider the problem of optimal transport from µ to ν with respect to a cost function c : X×Y → R. To ensure that the solution to this problem is smooth, it is necessary to make several assumptions about the structure of the domains and the cost function. In particular, Ma, Trudinger, and Wang [25] established regularity estimates when the domains are strongly relatively c-convex with respect to each other and the cost … Show more
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