Eigenvalue Estimates for Submanifolds with Locally Bounded Mean Curvature

By G. P. Bessa, M. Costa. 2002

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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 ∩ BN(p, r) in submanifolds M ⊂ϕNwith 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.

Subfields: Applied Mathematics, Mathematical Physics

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