# An overview of L1 optimal transportation on metric measure spaces

created by cavallett on 15 Jun 2016
modified on 24 Oct 2016

[BibTeX]

Preprint

Inserted: 15 jun 2016
Last Updated: 24 oct 2016

Year: 2016

Abstract:

The scope of this note is to make a self-contained survey of the recent developments and achievements of the theory of $L^{1}$-Optimal Transportation on metric measure spaces. Among the results proved in the recent papers \cite{CM1,CM2} 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 Levy-Gromov isoperimetric inequality.