Geometric and Functional Analysis

, Volume 18, Issue 5, pp 1696–1749 | Cite as

Weighted Sobolev Inequalities and Ricci Flat Manifolds



In this paper, we prove a weighted Sobolev inequality and a Hardy inequality on manifolds with nonnegative Ricci curvature satisfying a reverse volume doubling condition. It enables us to obtain rigidity results for Ricci flat manifolds.

AMS Mathematics Subject Classification:

53C21 53C25 46E35 

Keywords and phrases:

Sobolev and Hardy inequalities asymptotically flat manifolds Einstein manifolds 


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Copyright information

© Birkhaeuser 2009

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Jean LerayUMR CNRS 6629, Université de NantesNantes Cedex 3France

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