Eigenvalue estimates for submanifolds with locally bounded mean curvature in $N \times \mathbb {R}$

DOI10.1090/S0002-9939-08-09680-9zbMath1169.53045arXiv0804.4636MaRDI QIDQ3617600

M. Silvana Costa, Gregório Pacelli Bessa

Publication date: 30 March 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.4636

zbMATH Keywords

minimal submanifoldsfundamental tone estimatessubmanifolds with locally bounded mean curvature in \(N\times \mathbb {R}\)

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Spectral theory; eigenvalue problems on manifolds (58C40)

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ON SUBMANIFOLDS WITH TAMED SECOND FUNDAMENTAL FORM ⋮ The spectrum of the Laplacian and volume growth of proper minimal submanifolds ⋮ Gap theorems for submanifolds in \(\mathbb{H}^n\times\mathbb{R}\) ⋮ Eigenvalue estimates for the drifting Laplacian and the p-Laplacian on submanifolds of warped products ⋮ Eigenvalue estimates for submanifolds of warped product spaces ⋮ Estimates for eigenvalues of weighted Laplacian and weighted \(p\)-Laplacian

Cites Work

• Unnamed Item
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• An extension of Barta's theorem and geometric applications
• A complete minimal surface in \(R^ 3\) between two parallel planes
• Eigenvalue estimates for submanifolds with locally bounded mean curvature
• Adding handles to Nadirashvili's surfaces
• On compact \(H\)-hypersurfaces of \(N \times \mathbb{R}\)
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Stable minimal surfaces in \(M\times \mathbb R\)
• The theory of minimal surfaces in \(M\times \mathbb R\)
• Eigenvalue estimates for minimal surfaces in hyperbolic space
• Heat Equations on Minimal Submanifolds and Their Applications
• An Estimate for the Curvature of Bounded Submanifolds
• Complete nonorientable minimal surfaces in a ball of $\mathbb {R}^3$
• Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space
• A complete bounded minimal cylinder in \(\mathbb R^3\)
• Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces