Domains with Prescribed Automorphism Group

Abstract

Let G be the automorphism group of a bounded strictly pseudoconvex domain D⊂ℂN with a smooth ( \(\mathcal{C}^{\infty}\) ) boundary. Let H be a closed subgroup of G. Pertaining to the question whether it is possible to realize H as the automorphism group of a strictly pseudoconvex domain D′ which is an arbitrarily small perturbation of D in \(\mathcal{C}^{\infty}\) topology, we give a partial answer by describing sufficient conditions for D and G.