An overview of L1 Optimal Transportation on metric measure spaces
Metric Geometry
2018-09-14 v1
Abstract
The scope of this note is to make a self-contained survey of the recent developments and achievements of the theory of L1-Optimal Transportation on metric measure spaces. Among the results proved in the recent papers [20, 21] where the author, together with A. Mondino, proved a series of sharp (and in some cases rigid) geometric and functional inequalities in the setting of metric measure spaces enjoying a weak form of Ricci curvature lower bound, we review the proof of the L\'evy-Gromov isoperimetric inequality.
Keywords
Cite
@article{arxiv.1809.04859,
title = {An overview of L1 Optimal Transportation on metric measure spaces},
author = {Fabio Cavalletti},
journal= {arXiv preprint arXiv:1809.04859},
year = {2018}
}
Comments
Chapter of "Measure Theory in Non-Smooth Spaces", De Gruyter, Ed. Nicola Gigli