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arXiv · 1202.0333

On Open Scattering Channels for Manifolds with Ends

Rainer Hempel·Olaf Post·Ricardo Weder
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Abstract

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 (intrinsically and coordinate free) in purely geometric terms using the harmonic radius; therefore, the size of the perturbation can be controlled in terms of local bounds on the injectivity radius 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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Rainer Hempel, Olaf Post, Ricardo Weder. 2013-11-15. On Open Scattering Channels for Manifolds with Ends. https://doi.org/10.1016/j.jfa.2014.01.025

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