A note on the first nonzero eigenvalue of the Laplacian acting on p- forms

DOI10.1007/BF02568757zbMath0709.53031OpenAlexW1980131165MaRDI QIDQ921608

Gilles Courtois, Bruno Colbois

Publication date: 1990

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155520

zbMATH Keywords

Ricci curvaturediameterinjectivity radiusLaplaciannon-zero eigenvalueCheeger's isoperimetric constantp forms

Mathematics Subject Classification ID

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

Related Items (13)

Petites valeurs propres des fibrés principaux en tores ⋮ Spectrum of the Laplacian acting on differential \(p\)-forms, and down breaking handles ⋮ Manifolds with small Dirac eigenvalues are nilmanifolds ⋮ Petites valeurs propres et classe d'Euler des S1-fibrés ⋮ Elliptic PDEs on Compact Ricci Limit Spaces and Applications ⋮ Eigenvalues of the Laplacian acting on 𝑝-forms and metric conformal deformations ⋮ Collapsing, spectrum, and Diophantine properties of Riemannian flows ⋮ The gap of the eigenvalues for \(p\)-forms and harmonic \(p\)-forms of constant length ⋮ Eigenvalue and gap estimates for the Laplacian acting on 𝑝-forms ⋮ Remark about the spectrum of the 𝑝-form Laplacian under a collapse with curvature bounded below ⋮ Collapsing and the differential form Laplacian: the case of a smooth limit space. ⋮ A Cheeger-like inequality for coexact 1-forms ⋮ The \(p\)-spectrum of the Laplacian on compact hyperbolic three manifolds

Cites Work

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• The index of signature operators on Lipschitz manifolds
• Collapsing Riemannian manifolds while keeping their curvature bounded. II
• A lower bound for the first eigenvalue of a negatively curved manifold
• Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov. (On an isoperimetric inequality which generalizes that of Paul Lévy-Gromov)
• Collapsing Riemannian manifolds while keeping their curvature bounded. I
• Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne
• Beispiele zur Differentialtopologie von Singularitäten
• Gromov’s convergence theorem and its application
• On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold
• A note on the isoperimetric constant
• The Geometries of 3-Manifolds

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