Resonances on Some Geometrically Finite Hyperbolic Manifolds

DOI10.1080/03605300500361669zbMath1132.58019arXivmath/0412064OpenAlexW2015292998MaRDI QIDQ5291778

Colin Guillarmou

Publication date: 22 May 2006

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0412064

zbMATH Keywords

resolventresonanceshyperbolic manifoldscusps

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Scattering theory for PDEs (35P25)

Related Items (2)

Hyperfunctions in hyperbolic geometry ⋮ Resolvent of the Laplacian on geometrically finite hyperbolic manifolds

Cites Work

• Hodge theory on hyperbolic manifolds
• A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank
• Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
• The Laplace operator on hyperbolic three manifolds with cusps of non- maximal rank
• Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces
• Scattering asymptotics for Riemann surfaces
• Inverse scattering on asymptotically hyperbolic manifolds.
• Spectral geometry and scattering theory for certain complete surfaces of finite volume
• 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
• The Selberg zeta function and a local trace formula for Kleinian groups.
• The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix.

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