Scaling inequalities for spherical and hyperbolic eigenvalues

DOI10.4171/jst/447zbMath1526.35253OpenAlexW4385368640MaRDI QIDQ6062682

Jeffrey J. Langford, Richard Snyder Laugesen

Publication date: 6 November 2023

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jst/447

zbMATH Keywords

spherical capLaplace-Beltrami operatorLaplacianvibrating membranegeodesic diskDirichletNeumannCheng's inequality

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Cites Work

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• Sharp local estimates for the Szegő-Weinberger profile in Riemannian manifolds
• Eigenvalues variation. II: Multidimensional problems
• Upper bounds for eigenvalues of conformal metrics
• Bounds for the first eigenvalue of a spherical cap
• Eigenvalue comparison theorems and its geometric applications
• A note on Hayman's theorem on the bass note of a drum
• The spectrum of geodesic balls on spherically symmetric manifolds
• Eigenvalues of the Laplacian on balls with spherically symmetric metrics
• New features of the first eigenvalue on negatively curved spaces
• A second eigenvalue bound for the Dirichlet Schrödinger operator
• A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space
• Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues
• Upper and lower bounds for eigenvalues of the Laplacian on a spherical cap
• Existence et régularité de la fonction potentiel pour des écoulements subcritiques s'établissant autour d'un corps à singularité conique
• A sharp bound for the ratio of the first two Dirichlet eigenvalues of a domain in a hemisphere of 𝕊ⁿ
• Sharp Upper Bound to the First Nonzero Neumann Eigenvalue for Bounded Domains in Spaces of Constant Curvature
• Bifurcating Solutions of a Nonlinear Elliptic Neumann Problem on Large Spherical Caps
• Isoperimetric Inequality for Some Eigenvalues of an Inhomogeneous, Free Membrane
• Maximizers beyond the hemisphere for the second Neumann eigenvalue

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