Spectrum of the Laplacian acting on differential \(p\)-forms, and down breaking handles

DOI10.1007/BF01461004zbMath0909.58054MaRDI QIDQ1906489

Bruno Colbois, Colette Anné

Publication date: 10 March 1996

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165381

zbMATH Keywords

spectrumLaplaciandifferential \(p\)-forms

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20)

Related Items (15)

Nodal sets of Laplace eigenfunctions under small perturbations ⋮ Convergence of Dirichlet eigenvalues for elliptic systems on perturbed domains ⋮ Conformal minoration of the spectrum of the Hodge-de Rham Laplacian ⋮ Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian ⋮ Elliptic PDEs on Compact Ricci Limit Spaces and Applications ⋮ $p$-spectrum and collapsing of connected sums ⋮ Approximating orbifold spectra using collapsing connected sums ⋮ Convergence of spectra of graph-like thin manifolds ⋮ Construction of eigenvalues of multiplicity 2 of the Hodge-de Rham Laplacian ⋮ Unnamed Item ⋮ Gaps in the differential forms spectrum on cyclic coverings ⋮ Nondegeneracy of the eigenvalues of the Hodge Laplacian for generic metrics on 3-manifolds ⋮ The first eigenvalues of finite Riemannian covers ⋮ A Cheeger-like inequality for coexact 1-forms ⋮ Collapsing of connected sums and the eigenvalues of the Laplacian

Cites Work

• A note on the first nonzero eigenvalue of the Laplacian acting on p- forms
• Sur la multiplicité de la première valeur propre d'une surface de Riemann à courbure constante. (On the multiplicity of the first eigenvalue of a Riemannian surface of constant curvature)
• Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne
• The \(p\)-spectrum of the Laplacian on compact hyperbolic three manifolds
• Spectral sequences and adiabatic limits
• Hodge-Laplace operator on compact manifolds deprived of a finite number of balls.
• Fonctions Properes Sur Des Variétés Avec Des Anses Fines, Applcation À La Multiplicité
• Principe de Dirichlet pour les formes différentielles

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