$L^1$-Monge problem in metric spaces possibly with branching geodesics
Metric Geometry
2019-10-01 v1 Probability
Abstract
In this paper, we consider the Monge optimal transport problem with distance cost. We prove that in some metric spaces, possibly with many branching geodesics, an optimal transport map exists if the first marginal is absolutely continuous. The result is applicable to normed spaces and Hilbert geometries.
Keywords
Cite
@article{arxiv.1908.00772,
title = {$L^1$-Monge problem in metric spaces possibly with branching geodesics},
author = {Shinichiro Kobayashi},
journal= {arXiv preprint arXiv:1908.00772},
year = {2019}
}
Comments
19 pages, 1 figure