Some smooth applications of non-smooth Ricci curvature lower bounds

Andrea Mondino (Warwick, UK)

Abstract: After a brief introduction to the synthetic notions of 
Ricci curvature lower bounds in terms of optimal transportation, 
due to Lott-Sturm-Villani, I will discuss some applications to 
smooth Riemannian manifolds (joint work with Fabio Cavalletti, SISSA). 
These include: rigidity/stability of the Levy-Gromov inequality and an 
almost euclidean isoperimetric inequality motivated by the celebrated 
Perelman’s Pseudo-Locality Theorem for Ricci flow.