DAN

Abstract

I will introduce the notion of Ricci curvature for general Finsler manifolds. Bounding this curvature from below is equivalent to Lott, Sturm and Villani's curvature-dimension condition, and there are further applications (e.g., a Bochner-type formula and gradient estimates). I also would like to discuss some possible applications of this differential geometric technique to the geometry of Banach spaces.