On Open Scattering Channels for Manifolds with Ends

Details On Open Scattering Channels for Manifolds with Ends On Open Scattering Channels for Manifolds with Ends

2012-02-02

arxiv.org/abs/1202.0333v1

Physics

Mathematical Physics

Scientific paper

In the framework of time-dependent geometric scattering theory, we study the existence and completeness of the wave operators for perturbations of the Riemannian metric for the Laplacian on a complete manifold of dimension n. The smallness condition for the perturbation is expressed in purely geometric terms using the harmonic radius; therefore, the size of the perturbation can be controlled in terms of local bounds on the radius of injectivity and the Ricci-curvature. As an application of these ideas we obtain a stability result for the scattering matrix with respect to perturbations of the Riemannian metric. This stability result implies that a scattering channel which interacts with other channels preserves this property under small perturbations.

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