One dimensional weighted Ricci curvature and displacement convexity of entropies
One dimensional weighted Ricci curvature and displacement convexity of entropies
Abstract In the present paper, we prove that a lower bound on the 1âweighted Ricci curvature is equivalent to a convexity of entropies on the Wasserstein space. Based on such characterization, we provide some interpolation inequalities such as the PrĂŠkopaâLeindler inequality, the BorelâBranscampâLieb inequality, and the BrunnâMinkowski inequality under the âŚ