Friday, February 3, 2012

1202.0333 (Rainer Hempel et al.)

On Open Scattering Channels for Manifolds with Ends    [PDF]

Rainer Hempel, Olaf Post, Ricardo Weder
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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