Eigenvalue Estimates for Submanifolds with Locally Bounded Mean Curvature |
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Authors: | G. Pacelli Bessa J. Fábio Montenegro |
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Affiliation: | (1) Departamento de Matemática, Universidade Federal do Ceará, 60455760 Fortaleza-Ceará, Brazil |
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Abstract: | We present a method to obtain lower bounds for firstDirichlet eigenvalue in terms of vector fields with positivedivergence. Applying this to the gradient of a distance functionwe obtain estimates of eigenvalue of balls inside the cut locus and of domains M BN(p, r) in submanifolds M Nwith locally bounded mean curvature. Forsubmanifolds of Hadamard manifolds with bounded mean curvaturethese lower bounds depend only on the dimension of the submanifold and the bound on its mean curvature. |
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Keywords: | fundamental tone Dirichlet eigenvalue estimates Cheeger's constant locally bounded mean curvature |
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