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arXiv · 2011.09914

Weighted Sobolev Inequalities in CD(0,N) spaces

David Tewodrose
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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.

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David Tewodrose. 2020-11-19. Weighted Sobolev Inequalities in CD(0,N) spaces. https://arxiv.org/abs/2011.09914

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