Rigidity Results

• Mostow [19] established that finite co-volume discrete groups of PU(1,d) are rigid. The deformation theory of smaller groups, however, exhibits interesting phenomena.

• A theory of quasiconformal mapping on complex hyperbolic space and its boundary has been developed by Korányi, Riemann, Pansu and others. This theory plays a central role in Mostow's result.

• In particular, we have been able to show that smooth deformations of classical complex hyperbolic Schottky groups are quasiconformally stable.