Box distance and observable distance via optimal transport
Metric Geometry
2022-06-14 v2
Abstract
On the set of all metric measure spaces, we have two important metrics, the box metric and the observable metric, both introduced by M. Gromov. We obtain the representation of these metrics by using transport plan. In addition, we prove the existence of optimal transport plans of these metrics.
Cite
@article{arxiv.2204.04893,
title = {Box distance and observable distance via optimal transport},
author = {Hiroki Nakajima},
journal= {arXiv preprint arXiv:2204.04893},
year = {2022}
}
Comments
22 pages