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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