Data di Pubblicazione:
2014
Citazione:
Monge problem in metric measure spaces with Riemannian curvature-dimension condition / F. Cavalletti. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 99:(2014 Apr), pp. 136-151. [10.1016/j.na.2013.12.008]
Abstract:
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 RCD* (K, N), with N < infinity. For the first marginal measure, we assume that mu(0) << m. As a corollary, we obtain that the Monge problem and its relaxed version, the Monge-Kantorovich problem, attain the same minimal value. Moreover we prove a structure theorem for d-cyclically monotone sets: neglecting a set of zero m-measure they do not contain any branching structures, that is, they can be written as the disjoint union of the image of a disjoint family of geodesics.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Monge problem; Optimal transport; Ricci curvature; Riemannian curvature dimension condition;
Elenco autori:
F. Cavalletti
Link alla scheda completa:
Link al Full Text: