  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.
