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arXiv · 1809.04859

An overview of L1 Optimal Transportation on metric measure spaces

Fabio Cavalletti
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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.

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Fabio Cavalletti. 2018-09-13. An overview of L1 Optimal Transportation on metric measure spaces. https://arxiv.org/abs/1809.04859

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