  Take two isomorphic convex co-compact co-infinite volume Kleinian groups,
whose regular sets are diffeomorphic. The quotient of hyperbolic 3-space by
these groups gives two hyperbolic 3-manifolds whose scattering operators may be
compared. We prove that the operator norm of the difference between the
scattering operators is small, then the groups are related by a coorespondingly
small quasi-conformal deformation. This in turn implies that the two hyperbolic
3-manifolds are quasi-isometric.
