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Eigenvalue Estimates for Submanifolds with Locally Bounded Mean Curvature

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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 Ω ⊂ M ∩ B N (p, r) in submanifolds M ⊂ϕ 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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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Ceará, 60455760, Fortaleza-Ceará, Brazil

    G. Pacelli Bessa & J. Fábio Montenegro

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  1. G. Pacelli Bessa
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  2. J. Fábio Montenegro
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Bessa, G.P., Montenegro, J.F. Eigenvalue Estimates for Submanifolds with Locally Bounded Mean Curvature. Annals of Global Analysis and Geometry 24, 279–290 (2003). https://doi.org/10.1023/A:1024750713006

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