Weighted Sobolev Inequalities and Ricci Flat Manifolds
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- Minerbe, V. GAFA Geom. funct. anal. (2009) 18: 1696. doi:10.1007/s00039-009-0701-3
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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.