Calculus of Variations and Geometric Measure Theory

Optimal transport and quantitative geometric inequalities

Andrea Mondino (University of Oxford)

created by pinamonti on 25 Mar 2021

30 mar 2021 -- 14:30   [open in google calendar]

Zoom seminar

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The goal of the talk is to discuss a proof of the Levy-Gromov inequality for metric measure spaces (joint with Cavalletti), a quantitative version of the Levy- Gromov isoperimetric inequality (joint with Cavalletti and Maggi) as well as other geometricfunctional inequalities (joint with Cavalletti and Semola). Given a closed Riemannian manifold with strictly positive Ricci tensor, one estimates the measure of the symmetric difference of a set with a metric ball with the deficit in the Levy- Gromov inequality. The results are obtained via a quantitative analysis based on the localisation method via L1-optimal transport.