Eigenvalue Estimates for Submanifolds with Locally Bounded Mean Curvature

We present a method to obtain lower bounds for first Dirichlet eigenvalue in terms of vector fields with positive divergence. Applying this to the gradient of a distance function we obtain estimates of eigenvalue of balls inside the cut locus and of domains [Omega] [subset or is implied by] M [inter...

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Bibliographic Details
Published in:Annals of global analysis and geometry 2003-10, Vol.24 (3), p.279
Main Authors: G. Pacelli Bessa, Montenegro, J Fabio
Format: Article
Language:English
Subjects:
Boundary value problems
Eigenvalues
Estimates
Mathematical models
Methods
Statistical analysis
Studies
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Summary:We present a method to obtain lower bounds for first Dirichlet eigenvalue in terms of vector fields with positive divergence. Applying this to the gradient of a distance function we obtain estimates of eigenvalue of balls inside the cut locus and of domains [Omega] [subset or is implied by] M [intersection] BN(p, r) in submanifolds M [subset or is implied by][varphi] Nwith locally bounded mean curvature. For submanifolds of Hadamard manifolds with bounded mean curvature these lower bounds depend only on the dimension of the submanifold and the bound on its mean curvature. [PUBLICATION ABSTRACT]
ISSN:0232-704X
1572-9060
DOI:10.1023/A:1024750713006