Physics – Mathematical Physics
Scientific paper
2011-09-09
Physics
Mathematical Physics
Scientific paper
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity. Another condition is certain bounds of derivatives up to order one of the trace of this quantity. These conditions are shown to be optimal for existence and completeness of a wave operator. Our theory does not involve prescribed asymptotic behaviour of the metric at infinity (like asymptotic Euclidean or hyperbolic metrics studied previously in the literature). A consequence of the theory is spectral theory for the Laplace-Beltrami operator including identification of the continuous spectrum and absence of singular continuous spectrum.
Ito Katsushi
Skibsted Erik
No associations
LandOfFree
Scattering theory for Riemannian Laplacians does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Scattering theory for Riemannian Laplacians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scattering theory for Riemannian Laplacians will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-413173