Resonances for manifolds hyperbolic at infinity: optimal lower bounds on order of growth

Abstract

Suppose that $(X,g)$ is a conformally compact $(n+1)$-dimensional manifold that is hyperbolic at infinity in the sense that outside of a compact set $K\subset X$ the sectional curvatures of $g$ are identically equal to minus one. We prove that the counting function for the resolvent resonances has maximal order of growth $(n+1)$ generically for such manifolds.

28 pages, 1 figure

References in corpus (1)

• Several complex variables and the distribution of resonances in potential scattering