Large spectral gaps for Steklov eigenvalues under volume constraints and under localized conformal deformations

DOI10.1007/s10455-018-9612-6zbMath1405.58011arXiv1801.07836OpenAlexW2963146365MaRDI QIDQ1630073

Alexandre Girouard, Donato Cianci

Publication date: 7 December 2018

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

Full work available at URL: https://arxiv.org/abs/1801.07836

zbMATH Keywords

spectral gapspectral geometrySteklov spectrum

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 (8)

Tubular excision and Steklov eigenvalues ⋮ Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ From Steklov to Neumann via homogenisation ⋮ Steklov and Robin isospectral manifolds ⋮ Hypersurfaces with Prescribed Boundary and Small Steklov Eigenvalues ⋮ Large Steklov eigenvalues via homogenisation on manifolds ⋮ Laplace and Steklov extremal metrics via \(n\)-harmonic maps

Cites Work

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• Isoperimetric control of the Steklov spectrum
• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• Upper bounds for Steklov eigenvalues on surfaces
• Spectral geometry of the Steklov problem (survey article)
• Variational aspects of Laplace eigenvalues on Riemannian surfaces
• The Spectrum of a Riemannian Manifold with a Unit Killing Vector Field
• Optimal Shapes Maximizing the Steklov Eigenvalues

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