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