On the equivalence of distributional and synthetic Ricci curvature lower bounds

Abstract

The goal of the paper is to prove the equivalence of distributional and synthetic Ricci curvature lower bounds for a weighted Riemannian manifold with continuous metric tensor having Christoffel symbols in $L_{\mathrm{loc}}^2$, and with weight in $C^0\cap W_{\mathrm{loc}}^{1,2}$.

59 pages. Improved results with respect to V1. Final version accepted in Journ. Functional Analysis