On the lowest eigenvalue of the Hodge Laplacian on compact, negatively curved domains

DOI10.1007/s10455-008-9121-0zbMath1186.58021OpenAlexW2041589186MaRDI QIDQ1029594

Alessandro Savo

Publication date: 13 July 2009

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-008-9121-0

zbMATH Keywords

eigenvalueLaplacianconvex boundarystarlike domainabsolute boundary condition

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (12)

Estimates of the first Dirichlet eigenvalue from exit time moment spectra ⋮ New features of the first eigenvalue on negatively curved spaces ⋮ Lower bounds for the first Dirichlet eigenvalue of the Laplacian for domains in hyperbolic space ⋮ Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms ⋮ The first nonzero eigenvalue of the p-Laplacian on differential forms ⋮ Optimal lower eigenvalue estimates for Hodge-Laplacian and applications ⋮ On the first eigenvalue of the Dirichlet-to-Neumann operator on forms ⋮ On the fundamental tone of the \(p\)-Laplacian on Riemannian manifolds and applications ⋮ Extremal domains on Hadamard manifolds ⋮ Uncertainty principle on 3-dimensional manifolds of constant curvature ⋮ Optimal eigenvalue estimates for the Robin Laplacian on Riemannian manifolds ⋮ The vanishing of the fundamental gap of convex domains in \(\mathbb{H}^n\)

Cites Work

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• Function theory on manifolds which possess a pole
• The differential form spectrum of hyperbolic space
• Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne
• Spectra and eigenforms of the Laplacian on \(S^n\) and \(P^n(C)\)
• Hodge decomposition. A method for solving boundary value problems
• Partial differential equations. 1: Basic theory
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• Hodge-Laplace eigenvalues of convex bodies
• On the Differential Form Spectrum of Negatively Curved Riemannian Manifolds
• Eigenvalue and gap estimates for the Laplacian acting on 𝑝-forms
• SPECTRE DU LAPLACIEN DE HODGE–DE RHAM: ESTIMÉES SUR LES VARIÉTÉS CONVEXES

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