Scattering Matrix in Conformal Geometry

Abstract

This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. The conformally invariant powers of the Laplacian arise as residues of the scattering matrix and Branson's Q-curvature in even dimensions as a limiting value. The integrated Q-curvature is shown to equal a multiple of the coefficient of the logarithmic term in the renormalized volume expansion.