Compact manifolds with fixed boundary and large Steklov eigenvalues

DOI10.1090/proc/14426zbMath1483.58007arXiv1701.04125OpenAlexW2579832352WikidataQ127876356 ScholiaQ127876356MaRDI QIDQ5233960

Ahmad El Soufi, Bruno Colbois, Alexandre Girouard

Publication date: 9 September 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.04125

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (9)

Tubular excision and Steklov eigenvalues ⋮ Degenerating sequences of conformal classes and the conformal Steklov spectrum ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Multiple tubular excisions and large Steklov eigenvalues ⋮ From Steklov to Neumann via homogenisation ⋮ Sharp Steklov upper bound for submanifolds of revolution ⋮ The Steklov and Laplacian spectra of Riemannian manifolds with boundary ⋮ Hypersurfaces with Prescribed Boundary and Small Steklov Eigenvalues ⋮ Laplace and Steklov extremal metrics via \(n\)-harmonic maps

Cites Work

• Isoperimetric control of the Steklov spectrum
• Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem
• Sharp bounds for the first non-zero Stekloff eigenvalues
• A Cheeger inequality for the Steklov spectrum
• On a mixed Poincaré-Steklov type spectral problem in a Lipschitz domain
• The geometry of the first non-zero Stekloff eigenvalue
• Weyl-type bounds for Steklov eigenvalues
• Comparison of Steklov eigenvalues on a domain and Laplacian eigenvalues on its boundary in Riemannian manifolds
• The Steklov spectrum and coarse discretizations of manifolds with boundary
• The Steklov and Laplacian spectra of Riemannian manifolds with boundary
• Spectral geometry of the Steklov problem (survey article)
• Variational aspects of Laplace eigenvalues on Riemannian surfaces
• Eigenvalue inequalities for mixed Steklov problems
• Eigenvalues of the Laplacian on Forms
• The Steklov spectrum of surfaces: asymptotics and invariants

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