Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces

Ambrosio Luigi - Rajala Tapio

year: 2012
journal: Ann. Mat. Pura Appl.
abstract: We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics and we apply the latter to prove suitable generalizations of Brenier's theorem of existence of optimal maps.

The paper is available on the cvgmt preprint server.