Mathematics

The aim of the talk is to present some structural properties of the RCD spaces, which are metric measure spaces satisfying a lower Ricci curvature bound in a generalized sense. Mondino and Naber proved that any finite dimensional RCD space is rectifiable, namely that almost all of the space can be covered with countably many Borel sets that are biLipschitz equivalent to suitable subsets of the Euclidean space. By relying on some powerful results of De Philippis and Rindler, we will show how the reference measure of our RCD space behaves under those maps that have been built by Mondino and Naber. Finally, we will describe the relevant implications of such result on the structure of tangent spaces to RCD spaces. Joint work with N. Gigli.