Calculus of Variations and Geometric Measure Theory

A. Figalli - C. Villani

Strong displacement convexity on Riemannian manifolds

created by figalli on 16 Jan 2007
modified on 21 May 2007


Accepted Paper

Inserted: 16 jan 2007
Last Updated: 21 may 2007

Journal: Mathematische Zeitschrift
Year: 2007


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.