English

Existence and uniqueness of optimal maps on Alexandrov spaces

Differential Geometry 2007-05-23 v1 Analysis of PDEs

Abstract

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.

Keywords

Cite

@article{arxiv.0705.0437,
  title  = {Existence and uniqueness of optimal maps on Alexandrov spaces},
  author = {Jerome Bertrand},
  journal= {arXiv preprint arXiv:0705.0437},
  year   = {2007}
}