Resolvents, Poisson operators and scattering matrices on asymptotically hyperbolic and de Sitter spaces

DOI10.4171/JST/82zbMath1381.58014arXiv1303.5653MaRDI QIDQ2018370

András Vasy

Publication date: 14 April 2015

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

Full work available at URL: https://arxiv.org/abs/1303.5653

zbMATH Keywords

resolventsscattering matricesasymptotically hyperbolic spacesasymptotically de Sitter spacesasymptotically Minkowski spacesbackward and forward solution operator

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Scattering theory for PDEs (35P25) Wave equation (35L05) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (8)

Elliptic parametrices in the 0-calculus of Mazzeo and Melrose ⋮ The scattering matrix for 0th order pseudodifferential operators ⋮ Conformal extension of the Bunch-Davies state across the de Sitter boundary ⋮ Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes ⋮ On the positivity of propagator differences ⋮ Waves in the Witten bubble of nothing and the Hawking wormhole ⋮ Analytic continuation and high energy estimates for the resolvent of the Laplacian on forms on asymptotically hyperbolic spaces ⋮ The semiclassical resolvent on conformally compact manifolds with variable curvature at infinity

Cites Work

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• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov)
• Spectral geometry of singular Riemannian spaces
• The wave equation on asymptotically de Sitter-like spaces
• Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
• Einstein metrics with prescribed conformal infinity on the ball
• Scattering matrix in conformal geometry
• Inverse scattering on asymptotically hyperbolic manifolds.
• Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds
• Asymptotics of radiation fields in asymptotically Minkowski space
• Unique Continuation at Infinity and Embedded Eigenvalues for Asymptotically Hyperbolic Manifolds

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