Weighted Sobolev Inequalities in CD(0,N) spaces

2020/11/19 by David Tewodrose, Tewodrose, David
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2011.09914

openalex publication_date 2020/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove global weighted Sobolev inequalities on non-compact CD(0,N) spaces satisfying a suitable growth condition, extending to possibly non-smooth and non-Riemannian structures a previous result by V. Minerbe stated for Riemannian manifolds with non-negative Ricci curvature. We use this result in the context of RCD(0,N) spaces to get a uniform bound of the corresponding weighted heat kernel via a weighted Nash inequality.

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• On the parabolic kernel of the Schrödinger operator
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Quasiconformal maps in metric spaces with controlled geometry

Related

• Weighted Sobolev inequalities and Ricci flat manifolds
• Adimensional weighted Sobolev inequalities in PI spaces
• Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds
• Sobolev and isoperimetric inequalities for submanifolds in weighted\n ambient spaces
• Sobolev-Kantorovich inequalities under CD(0, ∞) condition