Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones

DOI10.4171/JST/416zbMath1498.35370arXiv1909.10842MaRDI QIDQ2080325

Magda Khalile, Vladimir Lotoreichik

Publication date: 7 October 2022

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.10842

zbMATH Keywords

2-manifoldlowest eigenvalueRobin Laplacianparallel coordinatesspectral isoperimetric inequalityunbounded conical domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05) PDEs on manifolds (35R01)

Related Items

Asymptotics of Robin eigenvalues on sharp infinite cones ⋮ Faber–Krahn inequalities for Schrödinger operators with point and with Coulomb interactions ⋮ The Robin Laplacian—Spectral conjectures, rectangular theorems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A spectral isoperimetric inequality for cones
• On Pólya's inequality for torsional rigidity and first Dirichlet eigenvalue
• On the negative spectrum of the Robin Laplacian in corner domains
• A variational approach to the isoperimetric inequality for the Robin eigenvalue problem
• Mean curvature bounds and eigenvalues of Robin Laplacians
• Some isoperimetric inequalities for membrane frequencies and torsional rigidity
• Eigenvalue comparison theorems and its geometric applications
• Friedlander's eigenvalue inequalities and the Dirichlet-to-Neumann semigroup
• Parallel coordinates in three dimensions and sharp spectral isoperimetric inequalities
• Optimisation of the lowest Robin eigenvalue in the exterior of a compact set. II: Non-convex domains and higher dimensions
• New eigenvalue estimates involving Bessel functions
• A sharp estimate for the first Robin-Laplacian eigenvalue with negative boundary parameter
• Optimal eigenvalue estimates for the Robin Laplacian on Riemannian manifolds
• The first Robin eigenvalue with negative boundary parameter
• On a conjectured reverse Faber-Krahn inequality for a Steklov-type Laplacian eigenvalue
• Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
• A Faber-Krahn inequality for Robin problems in any space dimension
• Le problème des isoperimetres sur les surfaces ouvertes à courbure positive
• From Steklov to Neumann and Beyond, via Robin: The Szegő Way
• On an Isoperimetric Inequality for the First Eigenvalue of a Boundary Value Problem
• Bonnesen-Style Isoperimetric Inequalities
• Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds
• On the Discrete Spectrum of Robin Laplacians in Conical Domains
• Optimisation of the lowest Robin eigenvalue in the exterior of a compact set
• Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian
• Extremal Domains and Pólya-type Inequalities for the Robin Laplacian on Rectangles and Unions of Rectangles
• The Robin Laplacian—Spectral conjectures, rectangular theorems
• Geodesic Parallel Coordinates in the Large
• 4 The Robin problem
• On the principal eigenvalue of a Robin problem with a large parameter
• Lower bounds for the nodal length of eigenfunctions of the Laplacian