Calculus of Variations and Geometric Measure Theory

F. Cavalletti

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.


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