Resumen de Strong displacement convexity on Riemannian manifolds

Alessio Figalli, Cédric Villani

• Ricci curvature bounds in Riemannian geometry are known to be equivalent to the weak convexity (convexity along at least one geodesic between any two points) of certain functionals in the space of probability measures. We prove that the weak convexity can be reinforced into strong (usual) convexity, thus solving a question left open in Lott and Villani (Ann of Math, to appear).