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Metric measure spaces with Riemannian Ricci curvature bounded from below

Infinite-Dimensional Geometry December 07, 2013 - December 08, 2013

December 08, 2013 (11:20 AM PST - 11:55 AM PST)
Speaker(s): Giuseppe Savare (Università di Pavia)
Location: Evans Hall
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract The talk will present some recent results, in collaboration with Luigi Ambrosio and Nicola Gigli, concerning various characterizations and properties of Riemannian metric measure spaces with a lower bound of the Ricci curvature. They can be defined starting from the Lott-Sturm-Villani approach by optimal transport and entropy, and assuming that the natural Cheeger energy form is quadratic. We will quickly overview the link with the induced Sobolev spaces, the Heat flow and the gradient flows in spaces of probability measures, the stability with respect to Sturm-Gromov-Hausdorff convergence, the localization and tensorization properties. The connections with the equivalent Bakry-Emery approach by Dirichlet forms and Gamma-calculus will also be discussed
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