Accepted Paper

Inserted: 9 feb 2024
Last Updated: 23 apr 2025

Journal: Journal of Functional Analysis
Year: 2024

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 $C^0\cap W^{1,2}_{{\rm loc}}$. The regularity assumptions are sharp, in the sense that they are minimal in order to define the distributional Ricci curvature tensor.

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