Eigenvalue estimates for submanifolds with locally bounded mean curvature

Abstract

We give lower bounds for the first Dirichilet eigenvalues for domains in submanifolds with locally bounded mean curvatures. These bounds depend on the injectivity radius, sectional curvature (upperbound) of the ambient space and on the mean curvature of the submanifold. For submanifolds fo Hadamard manifolds these lower bounds depend only on the dimension and mean curvature of the submanifold.

Paper writen in latex, 7 pages

Cited by in corpus (12)

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• Foliations and Chern-Heinz inequalities
• Eigenvalue Estimates for submanifolds of $N\times \mathbb{R}$ with locally bounded mean curvature
• On the spectrum of bounded immersions
• On the fundamental tone of the $p$-Laplacian on Riemannian manifolds and applications
• An Extension of Barta's Theorem and Geometric Applications
• Eigenvalue estimates for submanifolds of warped product spaces
• On cylindrically bounded $H$-Hypersurfaces of ${\mathbb{H}}^n\times \mathbb{R}$
• On the Entropies of Hypersurfaces with bounded mean curvature
• On the differential form spectrum of geometrically finite orbifolds
• Eigenvalue estimates for submanifolds in Hadamard manifolds and product manifolds $N\times \mathbb{R}$
• Riemannian submersions with discrete spectrum