Rigidity of conformally compact manifolds with the round sphere as the conformal infinity |
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Authors: | Satyaki Dutta |
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Institution: | a 8 Oakwood Ave, Norwalk, CT 06850, United States b 300 Summit Street, Department of Mathematics, Trinity College, Hartford, CT 06106, United States |
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Abstract: | In this paper, we prove that under a lower bound on the Ricci curvature and an assumption on the asymptotic behavior of the scalar curvature, a complete conformally compact manifold whose conformal boundary is the round sphere has to be the hyperbolic space. It generalizes similar previous results where stronger conditions on the Ricci curvature or restrictions on dimension are imposed. |
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Keywords: | Conformally compact metrics Ricci curvature Rigidity |
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