Ricci curvature and measures
This article is based on the 5th Takagi Lectures delivered by Jean-Pierre Bourguignon at the University of Tokyo on October 4 and 5, 2008. It offers the general reader -- even those of us not steeped in Differential Geometry -- a fascinating glimpse and interesting account of the development, during the last thirty years, of the analysis of spaces whose Ricci curvature admits a lower bound. Starting from the classical context, it highlights the interaction between three different fields in mathematics, namely optimal transport theory, Riemannian geometry and probability theory. It is very helpful for students and young researchers in mathematics and physics who want to see a broader picture of the evolution of idea in this topic.
scientific article; zbMATH DE number 5644706
scientific article