Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy

DOI10.1080/03605302.2015.1116561zbMath1351.58018arXiv1410.6881OpenAlexW1589231358MaRDI QIDQ2810607

Andrew Hassell, Xi Chen

Publication date: 3 June 2016

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

Full work available at URL: https://arxiv.org/abs/1410.6881

zbMATH Keywords

resolventasymptotically hyperbolic manifoldssemiclassical analysisFourier integral operatorintersecting Lagrangian distribution

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Pseudodifferential and Fourier integral operators on manifolds (58J40)

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Resolvent and Spectral Measure on Non-Trapping Asymptotically Hyperbolic Manifolds II: Spectral Measure, Restriction Theorem, Spectral Multipliers ⋮ On the equivalence of heat kernels of second-order parabolic operators ⋮ Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution ⋮ Local Smoothing Estimates for Schrödinger Equations on Hyperbolic Space ⋮ Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds. III: Global-in-time Strichartz estimates without loss ⋮ The heat kernel on asymptotically hyperbolic manifolds ⋮ X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds ⋮ Strichartz estimates and Strauss conjecture on non-trapping asymptotically hyperbolic manifolds ⋮ The scattering operator on asymptotically hyperbolic manifolds ⋮ Existence and Stability of Schrödinger Solitons on Noncompact Manifolds ⋮ Stability estimates for the X-ray transform on simple asymptotically hyperbolic manifolds ⋮ Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications

Cites Work

• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov)
• The Schrödinger propagator for scattering metrics
• Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
• The Hodge cohomology of a conformally compact metric
• Scattering matrix in conformal geometry
• The semiclassical resolvent and the propagator for non-trapping scattering metrics
• Fourier integral operators. I
• Fourier integral operators. II
• Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds
• Semi-Classical Wavefront Set and Fourier Integral Operators
• Lagrangian Intersection and the Cauchy Problem
• Unique Continuation at Infinity and Embedded Eigenvalues for Asymptotically Hyperbolic Manifolds
• Analytic Continuation and Semiclassical Resolvent Estimates on Asymptotically Hyperbolic Spaces
• The resolvent for Laplace-type operators on asymptotically conic spaces

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