Geometric spectral theory. Abstracts from the workshop held August 20--25, 2023

DOI10.4171/OWR/2023/36zbMATH Open1537.00026MaRDI QIDQ6544494

Author name not available (Why is that?)

Publication date: 27 May 2024

Published in: Oberwolfach Reports (Search for Journal in Brave)

Mathematics Subject Classification ID

Proceedings of conferences of miscellaneous specific interest (00B25) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Proceedings, conferences, collections, etc. pertaining to differential geometry (53-06) Second-order elliptic equations (35J15) Collections of abstracts of lectures (00B05) Differential geometric aspects of harmonic maps (53C43) Boundary value problems on manifolds (58J32) Proceedings, conferences, collections, etc. pertaining to partial differential equations (35-06) Proceedings, conferences, collections, etc. pertaining to global analysis (58-06) PDE constrained optimization (numerical aspects) (49M41)

Cites Work

• The Sound of Symmetry
• Heat content determines planar triangles
• On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian
• UNIFORM BOUNDS FOR EIGENFUNCTIONS OF THE LAPLACIAN ON MANIFOLDS WITH BOUNDARY*
• Hearing the Shape of a Triangle
• Comparison theorems for a class of first order Hamilton-Jacobi equations
• Remarks on courant's nodal line theorem
• From Steklov to Neumann and Beyond, via Robin: The Szegő Way
• Inégalités isopérimétriques et applications
• Symmetrization in a class of first-order Hamilton- Jacobi equations
• Multiple wells in the semi-classical limit I
• Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds
• On the Inner Radius of a Nodal Domain
• Pleijel’s nodal domain theorem for free membranes
• The Fate of the Landau Levels under Perturbations of Constant Sign
• A Topological Application of the Isoperimetric Inequality
• On Strong Barriers and an Inequality of Hardy for Domains in R ⁿ
• Construction de laplaciens dont une partie finie du spectre est donnée
• On the Eigenvalues of Vibrating Membranes^†
• Generic Properties of Eigenfunctions
• Regular and irregular semiclassical wavefunctions
• Multidimensional Reaction Diffusion Equations with Nonlinear Boundary Conditions
• On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space
• Sur la multiplicité de la première valeur propre de l’opérateur de Schrödinger avec champ magnétique sur la sphère
• On Neumann eigenfunctions in lip domains
• The “hot spots” conjecture for domains with two axes of symmetry
• Geometric and Computational Spectral Theory
• Scales, blow-up and quasimode constructions
• Sharp Upper Bound to the First Nonzero Neumann Eigenvalue for Bounded Domains in Spaces of Constant Curvature
• Stability and instability issues of the Weinstock inequality
• On Pleijel's Nodal Domain Theorem
• From Neumann to Steklov and beyond, via Robin: The Weinberger way
• On relations between principal eigenvalue and torsional rigidity
• Extremal Domains and Pólya-type Inequalities for the Robin Laplacian on Rectangles and Unions of Rectangles
• Lower Bound on Quantum Tunneling for Strong Magnetic Fields
• Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities
• Two balls maximize the third Neumann eigenvalue in hyperbolic space
• An optimization problem for finite point interaction families
• Upper bounds for higher-order Poincaré constants
• CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES
• QUANTITATIVE PROPAGATION OF SMALLNESS FOR SOLUTIONS OF ELLIPTIC EQUATIONS
• The Landau Hamiltonian with δ-potentials supported on curves
• Shape optimization for low Neumann and Steklov eigenvalues
• Wave Enhancement Through Optimization of Boundary Conditions
• The Robin Laplacian—Spectral conjectures, rectangular theorems
• Compact manifolds with fixed boundary and large Steklov eigenvalues
• Regularity for Shape Optimizers: The Degenerate Case
• On the principal eigenvalue of a Robin problem with a large parameter
• Isospectrality and heat content
• On a Theorem of Polya
• Isoperimetric Inequality for Some Eigenvalues of an Inhomogeneous, Free Membrane
• Transcendental Numbers. (AM-16)
• Shape optimization by the homogenization method
• Multiplicity of the Steklov spectrum on surfaces and the chromatic numbers
• The fate of Landau levels under \(\delta\)-interactions
• A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions
• Singular Weyl’s law with Ricci curvature bounded below
• Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons
• Geometric bounds for the magnetic Neumann eigenvalues in the plane
• Pólya's conjecture for Euclidean balls
• LOCALIZATION FOR THE TORSION FUNCTION AND THE STRONG HARDY INEQUALITY
• Weyl's law for the Steklov problem on surfaces with rough boundary
• Joint asymptotic expansions for Bessel functions
• A universal inequality for Neumann eigenvalues of the Laplacian on a convex domain in Euclidean space
• Maximizers beyond the hemisphere for the second Neumann eigenvalue
• A note on domain monotonicity for the Neumann eigenvalues of the Laplacian
• Some recent developments on the Steklov eigenvalue problem
• Shape optimization for combinations of Steklov eigenvalues on Riemannian surfaces
• Optimal bounds for Neumann eigenvalues in terms of the diameter
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• Asymptotic eigenvalue estimates for a Robin problem with a large parameter
• Extremal eigenvalues of the Laplacian on Euclidean domains and closed surfaces
• A geometric uncertainty principle with an application to Pleijel's estimate
• Faber-Krahn inequalities for the Robin-Laplacian: a free discontinuity approach
• Estimates of eigenvalues of the Laplacian by a reduced number of subsets
• Semiclassical analysis of low lying eigenvalues. II: Tunneling
• Spectral simplicity and asymptotic separation of variables
• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• On the asymptotic behaviour of the eigenvalues of a Robin problem.
• Eigenfunction and Bochner Riesz estimates on manifolds with boundary
• Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten
• An optimal Poincaré inequality for convex domains
• Domains without dense Steklov nodal sets
• Lower eigenvalue estimates for Dirac operators
• Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian
• Comparison results for elliptic and parabolic equations via Schwarz symmetrization
• A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
• Spectral methods in surface superconductivity
• On the role of convexity in isoperimetry, spectral gap and concentration
• Computations of the first eigenpairs for the Schrödinger operator with magnetic field
• The smallest Dirac eigenvalue in a spin-conformal class and cmc immersions
• Stationary partitioning of convex bodies
• Rearrangements and convexity of level sets in PDE
• Uniform domains
• Membranes élastiquement liées inhomogènes ou sur une surface: Une nouvelle extension de théorème isopérimétrique de Rayleigh-Faber- Krahn. (Inhomogeneously or on a surface elastically supported membranes: A new extension of the isoperimetric theorem of Rayleigh-Faber-Krahn)
• Berger's isoperimetric problem and minimal immersions of surfaces
• Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces
• On the first eigenvalue of the clamped plate
• Heat kernel estimates and lower bound of eigenvalues
• The essential spectrum of Neumann Laplacians on some bounded singular domains
• Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space
• Some inequalities between Dirichlet and Neumann eigenvalues
• Potential and scattering theory on wildly perturbed domains
• Some inequalities for Stekloff eigenvalues
• A counterexample to the ``hot spots conjecture
• On the ``hot spots conjecture of J. Rauch
• Convex symmetrization and applications
• Ein allgemeiner Satz zur Theorie der Eigenfunktionen selbstadjungierter Differentialausdrücke.
• Elliptic partial differential equations of second order
• Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic \(2\)-tori.
• Large spectral gaps for Steklov eigenvalues under volume constraints and under localized conformal deformations
• Short-time behavior of the heat kernel and Weyl's law on \(\mathrm{RCD}^*(K,N)\) spaces
• Lower bounds for the first eigenvalue of the magnetic Laplacian
• Optimal stretching for lattice points and eigenvalues
• Perturbation theory for linear operators.
• Maximum norms of chaotic quantum eigenstates and random waves
• Heat flow and Brownian motion for a region in \({\mathbb{R}}^ 2\) with a polygonal boundary
• Riemannian manifolds with uniformly bounded eigenfunctions
• On Rayleigh's conjecture for the clamped plate and its generalization to three dimensions
• Upper bounds for eigenvalues of the discrete and continuous Laplace operators
• Spectral gaps and rates to equilibrium for diffusions in convex domains
• Maximization of the second non-trivial Neumann eigenvalue
• Lower bounds for the first eigenvalue of the Laplacian with zero magnetic field in planar domains
• Effective operators for Robin eigenvalues in domains with corners
• The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities
• Globally diffeomorphic \(\sigma\)-harmonic mappings
• Large Steklov eigenvalues via homogenisation on manifolds
• The periodic Lieb-Thirring inequality
• Purely magnetic tunneling effect in two dimensions
• Efficiency and localisation for the first Dirichlet eigenfunction
• Erratum to: ``Euclidean triangles have no hot spots
• Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones
• Lowest energy band function for magnetic steps
• On efficiency and localisation for the torsion function
• Eigenfunction asymptotics and spectral rigidity of the ellipse
• Tunneling effect induced by a curved magnetic edge
• Faber-Krahn inequalities for the Robin Laplacian on bounded domain in Riemannian manifolds
• Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential
• Heat flow from polygons
• From Steklov to Neumann via homogenisation
• Index of minimal spheres and isoperimetric eigenvalue inequalities
• The Steklov spectrum and coarse discretizations of manifolds with boundary
• Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems
• Counting nodal domains in Riemannian manifolds
• Minimal 2-spheres in 3-spheres
• A sharp estimate for the first Robin-Laplacian eigenvalue with negative boundary parameter
• Euclidean triangles have no hot spots
• Some estimates for the higher eigenvalues of sets close to the ball
• Eigenvalues of the Laplacian on a compact manifold with density
• The first Robin eigenvalue with negative boundary parameter
• Steklov approximations of harmonic boundary value problems on planar regions
• Spectral geometry of the Steklov problem (survey article)
• Capacity and Faber-Krahn inequality in \(\mathbb R^{n}\)
• Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
• Nodal geometry, heat diffusion and Brownian motion
• Robin eigenvalues on domains with peaks
• On the lower bound of the inner radius of nodal domains
• Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space
• Pleijel's nodal domain theorem for Neumann and Robin eigenfunctions
• On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
• The Laplace-Beltrami operator in almost-Riemannian geometry
• Variational aspects of Laplace eigenvalues on Riemannian surfaces
• Laplacian eigenvalue functionals and metric deformations on compact manifolds
• A Faber-Krahn inequality for Robin problems in any space dimension
• Hypoelliptic second order differential equations
• The spectral function of an elliptic operator
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• On the heat content of a polygon
• Über das asymptotische Verhalten der Lösungen von \(\Delta u+\lambda u=0\) in unendlichen Gebieten
• Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds

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