  We show that complementary series of SO(n,1) which are sufficiently close to
a cohomological representation in the Fell topology, upon restriction to
SO(n-1,1), contain discretely, complementary series for SO(n-1,1) which are
also sufficiently close to cohomological representations.
  As a global application, we show that if the non-zero eigenvalues of the
Laplacian for differential forms of middle degree on congruence quotients of
the hyperbolic n-space remain bounded away from zero (for all even n), then
nonzero eigenvalues of the Laplacian on forms of arbitrary degree remain bonded
away from zero; this reduces conjectures of Clozel and Bergeron to the case of
middle degree forms.
