Semi-classical resolvent estimates for the Schr�dinger operator on non-compact complete Riemannian manifolds

Abstract

We prove uniform semi-classical estimates for the resolvent of the Schrodinger operator h 2Δ g + V (x), 0 0, where V is a real-valued non-negative potential and Δ g denotes the positive Laplace-Beltrami operator on a non-compact complete Riemannian manifold which may have a nonempty compact smooth boundary.