Weighted Sobolev Inequalities in CD(0,N) spaces
arXiv:2011.09914
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.
21 pages, 1 figure, to appear in ESAIM: COCV. A first version was available in 2017 on the French website https://hal.archives-ouvertes.fr