Accepted Paper

Inserted: 22 nov 2011
Last Updated: 14 nov 2012

Journal: Ann. Mat. Pura Appl.
Year: 2012

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.

Tags: GeMeThNES
Keywords: optimal transportation, geodesic metric space, non-branching, upper gradient

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