We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dL is a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show thatâ€¦ (More)

We will prove a decomposition for Wasserstein geodesics in the following sense: let (X, d,m) be a non-branching metric measure space verifying CDloc(K,N) or equivalently CD âˆ—(K,N). Then everyâ€¦ (More)

We prove the existence of solutions for the Monge minimization problem, addressed in a metric measure space (X, d,m) enjoying the Riemannian curvature-dimension condition RCDâˆ—(K,N), with N < âˆž. Forâ€¦ (More)

Abstract. For metric measure spaces verifying the reduced curvature-dimension condition CDâˆ—(K,N) we prove a series of sharp functional inequalities under the additional assumption of essentiallyâ€¦ (More)

We prove that if (X, d,m) is a metric measure space with m(X) = 1 having (in a synthetic sense) Ricci curvature bounded from below by K > 0 and dimension bounded above by N âˆˆ [1,âˆž), then the classicâ€¦ (More)

We address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussianâ€¦ (More)

Let (X, d,m) be a proper, non-branching, metric measure space. We show existence and uniqueness of optimal transport maps for cost written as non-decreasing and strictly convex functions of theâ€¦ (More)

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X, dN ) a possibly branching geodesic space. We showâ€¦ (More)

Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of of real valued Lipschitz function with non zero point-wise Lipschitzâ€¦ (More)

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X, dN ) a possibly branching geodesic space. We showâ€¦ (More)