On the extremality, uniqueness and optimality of transference plans

54 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Local curvature-dimension condition implies measure-contraction property (2011, background): “We recall the following version of the disintegration theorem that can be found on [3], Section 452 (see [2] for a direct proof).”
The Monge problem for strictly convex norms in Rd (2010, background): “Duality and sufficiency of cyclical monotonicity may be pursued in very general settings [23, 24, 25, 3, 26, 22, 8]; however for the purpose of this paper duality may be obtained more easily [1, 29].”
The globalization theorem for the Curvature-Dimension condition (2016, background): “and vice versa. We now formulate the Disintegration Theorem (it is formulated for probability measures but clearly holds for any ﬁnite non-zero measure): Theorem 6.18 (Theorem A.7, Proposition A.9 of [18]). Assume that (X,X ,m) is a countably generated probability space and that {Xα}α∈Q is a partiti”