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An overview of L1 Optimal Transportation on metric measure spaces. (arXiv:1809.04859v1 [math.MG])

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.查看全文

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