  Let G be a real reductive Lie group and H a closed reductive subgroup of G.
We investigate the deformation of "standard" compact quotients of G/H, i.e., of
quotients of G/H by discrete subgroups Gamma of G that are uniform lattices in
a closed reductive subgroup L of G acting properly and cocompactly on G/H. For
L of real rank 1, we prove that after a small deformation in G, such a group
Gamma remains discrete in G and its action on G/H remains properly
discontinuous and cocompact. More generally, we prove that the properness of
the action of any convex cocompact subgroup of L on G/H is preserved under
small deformations, and we extend this result to reductive homogeneous spaces
G/H over any local field. As an application, we obtain compact quotients of
SO(2n,2)/U(n,1) by Zariski-dense discrete subgroups of SO(2n,2) acting properly
discontinuously.

Group Theory