Studies of Some Curvature Operators in a Neighborhood of an Asymptotically Hyperbolic Einstein Manifold |
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Authors: | Erwann Delay |
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Institution: | Faculté des Sciences et Techniques, Laboratoire de Mathématiques, Parc de Grandmont, 37200, Tours, Francef1E-mail: delay@gargan.math.univ-tours.frf1 |
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Abstract: | On an asymptotically hyperbolic Einstein manifold (M,g0) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators of Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the metric g0. We deduce in the C∞ case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of g0. |
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Keywords: | Einstein manifold asymptotically hyperbolic curvatures of Riemann- Christoffel Ricci Einstein nonlinear PDE elliptic degenerate asymptotic behaviour |
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