Weighted Sobolev Inequalities in CD(0,N) spaces

Weighted Sobolev Inequalities in CD(0,N) spaces

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 t...

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1. Verfasser: Tewodrose, David
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Analysis of PDEs
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Zusammenfassung: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.
DOI:10.48550/arxiv.2011.09914