CR hypersurfaces with a contracting automorphism

Abstract

Let M be a real analytic CR hypersurface in Cn+1 admitting no varieties of positive dimension. We show first that every contracting local CR automorphism of M is linearizable. As a consequence, we show that such M admitting a contracting local CR automorphism is holomorphically equivalent to a weighted homogeneous hypersurface. Finally, we apply these results to prove that a bounded domain in Cn+1 with a real analytic boundary admitting an automorphism contracting at a boundary point must admit a Lie subgroup of real dimension at least two in its automorphism group.