Scattering Matrix in Conformal Geometry C. Robin Graham and Maciej Zworski

Scattering matrix in conformal geometry

1. Statement of the results This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. This connection is a manifestation of the general principle that the far field phenomena on a conformally compact Einstein manifold are related to conformal theories on its boundary...

Singular Part of the Scattering Matrix Determines the Obstacle

Mathematical Theory of Scattering Resonances

Correction and Supplements to “scattering Matrices and Scattering Geodesics of Locally Symmetric Spaces”

– This note corrects and complements our paper entitled “Scattering matrices and scattering geodesics of locally symmetric spaces” (Ann. Sci. Éc. Norm. Sup. 34 (2001) 441–469).  2002 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. – Nous apportons des corrections et des compléments à notre article intitulé “Scattering matrices and scattering geodesics of locally symmetric spaces” paru...

Q-curvature and Poincaré Metrics

This article presents a new definition of Branson’s Q-curvature in even dimensional conformal geometry. The Q-curvature is a generalization of the scalar curvature in dimension 2: it satisfies an analogous transformation law under conformal rescalings of the metric and on conformally flat manifolds its integral is a multiple of the Euler characteristic. Our approach is motivated by the recent w...