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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.

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  1. Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322, Nantes Cedex 3, France

    Vincent Minerbe

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  1. Vincent Minerbe
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Correspondence to Vincent Minerbe.

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

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Minerbe, V. Weighted Sobolev Inequalities and Ricci Flat Manifolds. GAFA Geom. funct. anal. 18, 1696–1749 (2009). https://doi.org/10.1007/s00039-009-0701-3

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  • DOI: https://doi.org/10.1007/s00039-009-0701-3

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