Geometric and Functional Analysis

, Volume 18, Issue 5, pp 1696–1749

Weighted Sobolev Inequalities and Ricci Flat Manifolds


DOI: 10.1007/s00039-009-0701-3

Cite this article as:
Minerbe, V. GAFA Geom. funct. anal. (2009) 18: 1696. doi:10.1007/s00039-009-0701-3


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:


Keywords and phrases:

Sobolev and Hardy inequalitiesasymptotically flat manifoldsEinstein manifolds

Copyright information

© Birkhaeuser 2009

Authors and Affiliations

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