Existence and uniqueness of optimal maps on Alexandrov spaces

Details Existence and uniqueness of optimal maps on Alexandrov spaces Existence and uniqueness of optimal maps on Alexandrov spaces

2007-05-03

arxiv.org/abs/0705.0437v1

Mathematics

Differential Geometry

Scientific paper

The purpose of this paper is to show that in a finite dimensional metric
space with Alexandrov's curvature bounded below, Monge's transport problem for
the quadratic cost admits a unique solution.

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