Verifications of the Scattering Theory on Manifolds

Abstract

Scattering theory plays the main role in the study of manifolds and the Laplacian spectrum. In this article, we process justifying the continuous Laplacian spectrum and on a complete Riemannian manifold. ( M , g i ) is categorized by the use of bounded curvature of the metric. In particular, the covariant derivative is limitedly considered as an application in the geodesic distance from a fixed point.