Nonnegative Ricci curvature and Poincaré inequalities

Herve Pajot

(Université de Grenoble)

Event: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Date: Oct 13, 2011, time: 16:50

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. A famous result in geometric analysis states that any Riemannian manifold with nonnegative Ricci curvature supports a Poincaré inequality. In this talk, we will discuss (possible) extensions of this result to various settings, for instance (discrete) graphs and (continuous) geodesic spaces. In these situations, the Ricci curvature condition will be expressed in terms of optimal transportation, the Bakry-Emery inequality for elliptic operators, or the Brunn-Minkowski inequality.