Domains with Prescribed Automorphism Group

Abstract

Let G be the automorphism group of a bounded strictly pseudoconvex domain D subset of C(N) with a smooth (C(infinity)) 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 C(infinity) topology, we give a partial answer by describing sufficient conditions for D and G.