Higher order scattering on asymptotically Euclidean Manifolds

2000/02/17 by T. J. Christiansen, Christiansen, T. J., M. S. Joshi +2
Mathematics · Physics and Astronomy · #35P25 #58J20 #58J40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #math.SP #msc:35P25 #msc:58J20 #msc:58J40

paper · pdf · doi:10.48550/arxiv.math/0002148

To appear in the Canadian Journal of Mathematics; 26 pages

arxiv created 2000/02/17 · openalex publication_date 2000/02/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time πon the boundary. Furthermore, it is shown that on \Realⁿ the asymptotics of certain short-range perturbations of Δ^k can be recovered from the scattering matrix at a finite number of energies.

Related

• The scattering operator on asymptotically hyperbolic manifolds
• Inverse Scattering on Asymptotically Hyperbolic Manifolds
• Microlocal properties of scattering matrices for Schrödinger equations on scattering manifolds
• Scattering and Inverse Scattering on ACH Manifolds
• Scattering theory for the Laplacian on manifolds with bounded curvature