Bipolar comparison
Differential Geometry
2019-04-22 v4 Metric Geometry
Abstract
We define a new type of metric comparison similar to the comparison of Alexandrov. We show that it has strong connections to continuity of optimal transport between regular measures on a Riemannian manifold, in particular to the so called MTW condition introduced by Xi-Nan Ma, Neil Trudinger and Xu-Jia Wang.
Cite
@article{arxiv.1711.09423,
title = {Bipolar comparison},
author = {Nina Lebedeva and Anton Petrunin and Vladimir Zolotov},
journal= {arXiv preprint arXiv:1711.09423},
year = {2019}
}
Comments
25 pages, 16 figures