Optimal transport maps on Alexandrov spaces revisited
Metric Geometry
2018-04-04 v2 Analysis of PDEs
Differential Geometry
Abstract
We give an alternative proof for the fact that in -dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely -unrectifiable starting measure, and that this plan is induced by an optimal map.
Keywords
Cite
@article{arxiv.1803.10023,
title = {Optimal transport maps on Alexandrov spaces revisited},
author = {Tapio Rajala and Timo Schultz},
journal= {arXiv preprint arXiv:1803.10023},
year = {2018}
}
Comments
16 pages. Added a reference to an earlier proof of the result by Bertrand