کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6415183 | 1334962 | 2014 | 58 صفحه PDF | دانلود رایگان |
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.
Journal: Journal of Functional Analysis - Volume 266, Issue 9, 1 May 2014, Pages 5526-5583