On the equivalence of distributional and synthetic Ricci curvature lower bounds

2024/02/09 by Andrea Mondino, Mondino, Andrea, Vanessa Ryborz +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2402.06486

openalex publication_date 2024/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L²_{\rm loc}, and with weight in C⁰∩ W^1,2_{\rm loc}.

Cited by

• The infinitesimal structure of manifolds with non-continuous Riemannian metrics

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