In\'egalit\'e de Sobolev et volume asymptotique
Differential Geometry
2014-06-13 v1
Abstract
A result of M. Ledoux is that a complete Riemannian manifold with non negative Ricci curvature satisfying the Euclidean Sobolev inequality is the Euclidean space. We present a shortcut of the proof. We also give a refinement of a result of B-L. Chen et X-P. Zhu about locally conformally flat manifolds with non negative Ricci curvature. Eventually, we discuss Ledoux's result when the hypothesis on the Ricci curvature is weakened on a hypothesis on the scalar curvature.
Cite
@article{arxiv.1107.5887,
title = {In\'egalit\'e de Sobolev et volume asymptotique},
author = {Gilles Carron},
journal= {arXiv preprint arXiv:1107.5887},
year = {2014}
}