Supervisors info:
Παναγιώτης Γιαννιώτης, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Summary:
After reminding some basic elements of Riemannian Geometry, we will make an introduction to the basics of optimal transport theory on Riemannian manifolds. The main result presented is the equivalence of a lower bound for Ricci curvature with the K-convexity of the relative entropy, a functional on the space of absolutely continuous (w.r.t. vol_g) probability measures. This equivalence allows the definition of lower Ricci bounds on metric measure spaces, where the Riemannian structure is absent.
Keywords:
ricci,curvature,optimal,transport,riemman,geometry,differential,manifold,manifolds,metric,measure,geodesic,geodesics,curve,curves,sectional,tensor
