On the Equivalence of Distributional and Synthetic Ricci Curvature Lower Bounds

Explore a mathematical lecture where Vanessa Ryborz discusses the equivalence between distributional and synthetic approaches to defining Ricci curvature lower bounds on manifolds with low regularity. Learn how to address the challenge of computing Ricci curvature tensors on manifolds with Riemannian metrics below C^2 regularity through two alternative methods: distribution theory on manifolds and the CD(K,N)-condition (a synthetic notion introduced by Lott-Villani and Sturm that generalizes manifolds with Ricci curvature bounded below by K and dimension bounded above by N). Discover the joint research with Andrea Mondino that proves these two definitions are equivalent for manifolds with continuous Riemannian metrics allowing locally 2-integrable connections. This 58-minute lecture from the Hausdorff Center for Mathematics provides valuable insights into advanced differential geometry concepts.