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

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

2011-11-22

arxiv.org/abs/1111.5119v1

Mathematics

Metric Geometry

19 pages, 2 figures

Scientific paper

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.

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