A Reilly formula and eigenvalue estimates for differential forms

DOI10.1007/s12220-010-9161-0zbMath1228.58018arXiv1003.0817OpenAlexW3106020909WikidataQ115376909 ScholiaQ115376909MaRDI QIDQ555697

Alessandro Savo, Simon Raulot

Publication date: 26 July 2011

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.0817

zbMATH Keywords

eigenvaluerigidity resultscompact manifold with boundarydifferential \(p\)-formsReilly-type formulaspectrum of the Hodge Laplacian

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Differential forms in global analysis (58A10) Rigidity results (53C24)

Related Items (20)

Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary ⋮ Some sharp Hodge Laplacian and Steklov eigenvalue estimates for differential forms ⋮ Trace and inverse trace of Steklov eigenvalues ⋮ Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary. II ⋮ On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain ⋮ Eigenvalue estimates of Reilly type in product manifolds and eigenvalue comparison for strip domains ⋮ A higher dimensional generalization of Hersch-Payne-Schiffer inequality for Steklov eigenvalues ⋮ On the first eigenvalue of the 𝑝-Laplacian on Riemannian manifolds ⋮ On the best constant in Gaffney inequality ⋮ Cohomology vanishing theorems for free boundary submanifolds ⋮ A Poincaré formula for differential forms and applications ⋮ Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms ⋮ Estimates for higher Steklov eigenvalues ⋮ 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 ⋮ Eigenvalue and gap estimates of isometric immersions for the Dirichlet-to-Neumann operator acting on \(p\)-forms ⋮ Rigidity results for spin manifolds with foliated boundary ⋮ Trace and inverse trace of Steklov eigenvalues. II. ⋮ On the eigenforms of compact stratified spaces

Cites Work

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• Rigidity of compact Riemannian spin manifolds with boundary
• A first eigenvalue estimate for minimal hypersurfaces
• Extrinsic spheres in a Kähler manifold
• Compact hypersurfaces with constant higher order mean curvatures
• Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein
• Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne
• Extrinsic Killing spinors
• Conformal Killing forms on Riemannian manifolds
• On a Riemannian space admitting more than one Sasakian structures
• Harmonic tensors on Riemannian manifolds with boundary
• Rigidity of compact manifolds with boundary and nonnegative Ricci curvature
• Eigenvalue and gap estimates for the Laplacian acting on 𝑝-forms
• Totally umbilical hypersurfaces of a locally product Riemannian manifold
• Dirac operator on embedded hypersurfaces

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