Diffusion, Optimal Transport and Ricci Curvature for Metric Measure Space

[摘要] Lower Ricci curvature bounds play a crucial role in severaldeep geometric and functional inequalities in Riemannian geometry and diffusion processes. Bakry–Émery [8] introducedan elegant and powerful technique, based on commutator estimates for differential operators and so-called Γ-calculus, toderive many sharp results. Their curvature-dimension condition has been further developed by many authors, mainly inthe framework of Markov diffusion modelled on weighted Riemannian manifolds, with relevant applications to infinite dimensional problems.