Scattering metrics and geodesic flow at infinity
type: Item
instance of: scholarly article
title: Scattering metrics and geodesic flow at infinity
zbMATH Open document ID: 0855.58058
author: Maciej Zworski
author: Richard Melrose
published in: Inventiones Mathematicae
publication date: 1996-04-16T00:00:00Z
full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary
review text: Any compact \(C^\infty\) manifold with boundary admits a so-called scattering metric on its interior. In a previous work, the first author discussed the scattering theory of the corresponding Laplacian. In the present work, it is proved, as conjectured, that the scattering matrix is a Fourier integral operator which quantizes the geodesic flow on the boundary (for a metric defined canonically by the scattering metric) at time \(\pi\). This is proved by showing that the Poisson operator of the associated generalized boundary problem is a Fourier integral operator associated to a singular Legendre manifold.
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35S30
zbMATH DE Number: 866097
zbMATH Keywords: scattering metric
zbMATH Keywords: Fourier integral operator
zbMATH Keywords: geodesic flow
reviewed by: Paul Godin
MaRDI profile type: Publication
OpenAlex ID: W2044076457
DOI: 10.1007/S002220050058
description: scientific article; zbMATH DE number 866097