, Volume 18, Issue 5, pp 1696-1749

Weighted Sobolev Inequalities and Ricci Flat Manifolds

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.

Received: November 2006, Revision: April 2007, Accepted: April 2007