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Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold

Abstract : We establish inequalities for the eigenvalues of the sub-Laplace operator associated with a pseudo-Hermitian structure on a strictly pseudoconvex CR manifold. Our inequalities extend those obtained by Niu and Zhang \cite{NiuZhang} for the Dirichlet eigenvalues of the sub-Laplacian on a bounded domain in the Heisenberg group and are in the spirit of the well known Payne-P\'{o}lya-Weinberger and Yang universal inequalities.
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Submitted on : Monday, January 28, 2013 - 7:30:20 AM
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Amine Aribi, Ahmad El Soufi. Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2012, 47 (3-4), pp.437-463. ⟨10.1007/s00526-012-0523-2⟩. ⟨hal-00779283⟩

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