A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space

DOI10.1215/S0012-7094-07-14022-5zbMath1189.58014arXivmath-ph/0511045OpenAlexW1993636109WikidataQ59158114 ScholiaQ59158114MaRDI QIDQ2461386

Rafael D. Benguria, Helmut Linde

Publication date: 27 November 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0511045

zbMATH Keywords

hyperbolic spaceDirichlet LaplacianDirichlet spectrumcenter of massPayne-Pólya-Weinberger conjectureBaumgartner-Grosse-Martin inequalityChiti's comparison result

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items (12)

Two balls maximize the third Neumann eigenvalue in hyperbolic space ⋮ A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on 𝑅𝐶𝐷(𝐾,𝑁) spaces ⋮ Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator ⋮ The PPW conjecture in curved spaces ⋮ Scaling inequalities for spherical and hyperbolic eigenvalues ⋮ The abstract Birman-Schwinger principle and spectral stability ⋮ Maximizers beyond the hemisphere for the second Neumann eigenvalue ⋮ Talenti's comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature ⋮ Well-posedness of Hersch-Szegő's center of mass by hyperbolic energy minimization ⋮ Eigenvalue pinching on convex domains in space forms ⋮ On the Ashbaugh-Benguria conjecture about lower-order Dirichlet eigenvalues of the Laplacian ⋮ The vanishing of the fundamental gap of convex domains in \(\mathbb{H}^n\)

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