Fractal Weyl laws for asymptotically hyperbolic manifolds

DOI10.1007/s00039-013-0225-8zbMath1297.58006arXiv1206.2255OpenAlexW2079303608MaRDI QIDQ359555

Kiril Datchev, Semyon Dyatlov

Publication date: 12 August 2013

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.2255

zbMATH Keywords

resonancesSelberg zeta functionhyperbolic manifoldsHamiltonian flowWeyl lawMinkowski dimensiontrapped geodesicsescape functions

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Scattering theory for PDEs (35P25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Pseudodifferential and Fourier integral operators on manifolds (58J40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Resonance in context of PDEs (35B34) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (17)

Resonances for open quantum maps and a fractal uncertainty principle ⋮ Sharp Weyl estimates for tensor products of pseudodifferential operators ⋮ A note on the resonance counting function for surfaces with cusps ⋮ Spectral gaps, additive energy, and a fractal uncertainty principle ⋮ Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics ⋮ Uniform hyperbolicity of a class of scattering maps ⋮ Weyl laws for open quantum maps ⋮ Fractal Weyl laws and wave decay for general trapping ⋮ Fractal Weyl law for open quantum chaotic maps ⋮ Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps ⋮ Resonances for asymptotically hyperbolic manifolds: Vasy's method revisited ⋮ Mathematical study of scattering resonances ⋮ Distribution of Resonances for Hyperbolic Surfaces ⋮ Resonance projectors and asymptotics for 𝑟-normally hyperbolic trapped sets ⋮ Microlocal analysis of forced waves ⋮ Control of eigenfunctions on surfaces of variable curvature ⋮ Decay of correlations for normally hyperbolic trapping

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov)
• Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes
• From open quantum systems to open quantum maps
• Lower bounds for resonances of infinite-area Riemann surfaces
• Resolvent estimates for normally hyperbolic trapped sets
• Resolvent of the Laplacian on geometrically finite hyperbolic manifolds
• Polynomial bound on the number of scattering poles
• Fractal upper bounds on the density of semiclassical resonances
• Distribution of resonances for open quantum maps
• Geometric bounds on the density of resonances for semiclassical problems
• Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
• Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
• Semiclassical resonances generated by a closed trajectory of hyperbolic type
• Hausdorff dimension of quasi-circles
• The density at infinity of a discrete group of hyperbolic motions
• The limit set of a Fuchsian group
• Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group
• Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces
• Distribution of resonances for spherical black holes
• Scattering asymptotics for Riemann surfaces
• Hausdorff dimension and Kleinian groups
• Scattering matrix in conformal geometry
• The Selberg zeta function for convex co-compact Schottky groups
• Semiclassical estimates in asymptotically Euclidean scattering
• Distribution of resonances for asymptotically Euclidean manifolds
• Resonances and scattering poles on asymptotically hyperbolic manifolds
• The divisor of Selberg's zeta function for Kleinian groups. Appendix A by Charles Epstein
• Upper bounds on the number of resonances for non-compact Riemann surfaces
• Partial differential equations. 2: Qualitative studies of linear equations
• Propagation through trapped sets and semiclassical resolvent estimates
• Fractal Weyl law for open quantum chaotic maps
• Density and location of resonances for convex co-compact hyperbolic surfaces
• Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds
• Scattering poles for asymptotically hyperbolic manifolds
• Spectral problems in open quantum chaos
• Prequantum transfer operator for symplectic Anosov diffeomorphism
• Semi-Classical Wavefront Set and Fourier Integral Operators
• The zeta functions of Ruelle and Selberg. I
• Espaces fonctionnels associés au calcul de Weyl-Hörmander
• Microlocal limits of plane waves and Eisenstein functions
• Resonance projectors and asymptotics for 𝑟-normally hyperbolic trapped sets
• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
• Riemannian geometry
• Notions of convexity

This page was built for publication: Fractal Weyl laws for asymptotically hyperbolic manifolds