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 $L^2_{{\rm loc}}$, and with weight in $C^0\cap W^{1,2}_{{\rm loc}}$.