### Some smooth applications of non-smooth Ricci curvature lower bounds

Analysis and Geometry Seminar

24th April 2018, 3:00 pm – 4:00 pm

Howard House, 2nd Floor Seminar Room

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. These include: rigidity and stability of Levy-Gromov inequality, an almost euclidean isoperimetric inequality motivated by the celebrated Perelman’s Pseudo-Locality Theorem for Ricci flow, and some geometric properties of quotients of smooth manifolds having Ricci curvature bounded below.

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