Scattering theory for conformally compact metrics with variable curvature at infinity
Abstract
We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L2 decay in directions where the asymptotic curvature is sufficiently negative. The scattering matrix is shown to be a pseudodifferential operator. For generic frequency in this part of the continuous spectrum, we give an explicit construction of the resolvent kernel.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.