Heat invariants of the Steklov problem

DOI10.1007/s12220-013-9451-4zbMath1432.58026arXiv1304.7233OpenAlexW1989480962MaRDI QIDQ2347933

Iosif Polterovich, David A. Sher

Publication date: 10 June 2015

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

Full work available at URL: https://arxiv.org/abs/1304.7233

zbMATH Keywords

Riemannian manifoldDirichlet-to-Neumann operatorheat traceSteklov problemspectral rigidity

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Pseudodifferential and Fourier integral operators on manifolds (58J40) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (20)

The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript ⋮ Asymptotics of sloshing eigenvalues for a triangular prism ⋮ Spectral invariants of the perturbed polyharmonic Steklov problem ⋮ Shape optimization for the Steklov problem in higher dimensions ⋮ Gluing formula for Casimir energies ⋮ The BFK-gluing formula and the curvature tensors on a 2-dimensional compact hypersurface ⋮ A characterization of the disk by eigenfunction of the Steklov eigenvalue ⋮ Spectral invariants of the magnetic Dirichlet-to-Neumann map on Riemannian manifolds ⋮ Classification of some geometric structures on 4-dimensional Riemannian Lie group ⋮ Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Geometric invariants of spectrum of the Navier-Lamé operator ⋮ On the relative heat invariants of the Dirichlet-to-Neumann operators associated with Schrödinger operators ⋮ Evaluation algorithm of root canal shape based on Steklov spectrum analysis ⋮ The gluing formula, conformal scaling, and geometry ⋮ The Steklov and Laplacian spectra of Riemannian manifolds with boundary ⋮ Steklov and Robin isospectral manifolds ⋮ The BFK-gluing formula for zeta-determinants and the conformal rescaling of a metric ⋮ Spectral invariants of Dirichlet-to-Neumann operators on surfaces ⋮ THE STEKLOV SPECTRUM OF CUBOIDS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp eigenvalue bounds and minimal surfaces in the ball
• Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces
• Isoperimetric control of the Steklov spectrum
• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• Upper bounds for Steklov eigenvalues on surfaces
• Some asymptotic formulas for elliptic pseudodifferential operators
• An inverse spectral result for the Neumann operator on planar domains
• The spectrum of positive elliptic operators and periodic bicharacteristics
• The Radon transform on Zoll surfaces
• Maximally degenerate Laplacians
• Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems
• Partial differential equations. 2: Qualitative studies of linear equations
• Resonant rigidity of \(S^2\)
• Prescription of the Steklov spectrum within a conformal class
• Eigenvalues of the Laplacian of Riemannian manifolds
• Sharp upper bound and a comparison theorem for the first nonzero Steklov eigenvalue
• CONSTANT HIGHER-ORDER MEAN CURVATURE HYPERSURFACES IN RIEMANNIAN SPACES
• Determining anisotropic real-analytic conductivities by boundary measurements
• Determinant of the Neumann Operator on Smooth Jordan Curves
• Logarithmic terms in asymptotic expansions of heat operator traces
• Burghelea-Friedlander-Kappeler’s gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion
• Combinatorics of the Heat Trace on Spheres
• Shape optimization for low Neumann and Steklov eigenvalues

This page was built for publication: Heat invariants of the Steklov problem