Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below
Differential Geometry
2013-05-22 v1 Metric Geometry
Abstract
We prove existence and uniqueness of optimal maps on spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation.
Keywords
Cite
@article{arxiv.1305.4849,
title = {Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below},
author = {Nicola Gigli and Tapio Rajala and Karl-Theodor Sturm},
journal= {arXiv preprint arXiv:1305.4849},
year = {2013}
}
Comments
10 pages