Polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in \(\mathbb{R}^ n, n\geq{}3\), odd (Q1191045)

The author obtains an upper bound for the number of scattering poles of compactly supported metric perturbations of the Laplacian in \(\mathbb{R}^ n\). More precisely, one gets that the number of such poles inside the ball of radius \(r\) is bounded by a constant times \(r^{n+1}\) as \(r\) tends to infinity. For this purpose, the author proves sharp estimates on the cut-off resolvent of the free Laplacian and uses the Phragmen- Lindelöf principle.