On the fundamental tone of immersions and submersions

DOI10.1090/proc/13969zbMath1390.35201arXiv1306.1559OpenAlexW2962783971MaRDI QIDQ4636750

Fernando Manfio, Marcos Petrúcio De A. Cavalcante

Publication date: 20 April 2018

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

Full work available at URL: https://arxiv.org/abs/1306.1559

zbMATH Keywords

eigenvaluesisometric immersionsmean curvatureRiemannian submersions

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Global Riemannian geometry, including pinching (53C20)

Related Items (4)

On the Steklov spectrum of covering spaces and total spaces ⋮ Spectral estimates for Riemannian submersions with fibers of basic mean curvature ⋮ On the fundamental tone of the \(p\)-Laplacian on Riemannian manifolds and applications ⋮ Spectral estimates and discreteness of spectra under Riemannian submersions

Cites Work

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• Curvature estimates for submanifolds immersed into horoballs and horocylinders
• Eigenvalue estimates for hypersurfaces in \(\mathbb H^{m} \times \mathbb R\) and applications
• Isoperimetric inequalities on minimal submanifolds of space forms
• Riemannian submersions with totally geodesic fibers
• On the stability operator of submanifolds with constant mean curvature in hyperbolic space
• Eigenvalue estimates for submanifolds with locally bounded mean curvature
• A remark on the inequality of McKean
• The fundamental equations of a submersion
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space

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