, Volume 18, Issue 5, pp 1696-1749

Weighted Sobolev Inequalities and Ricci Flat Manifolds

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Abstract.

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