Several complex variables and the order of growth of the resonance counting function in Euclidean scattering

Abstract

We study four classes of compactly supported perturbations of the Laplacian on Rd, d ≥ 3 odd. They are a fairly general class of black box perturbations, a class of second order, self-adjoint elliptic differential operators, Laplacians associated to metric perturbations, and the Dirichlet Laplacian on the exterior of a star-shaped obstacle. In each case, we show that generically the resonance counting function has maximal order of growth.