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.
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Communicated by Steven Krantz.
This research was supported by the Grant KRF-2002-070-C00005 (PI:K.T.Kim) from the Korea Research Foundation.
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Min, BL. Domains with Prescribed Automorphism Group. J Geom Anal 19, 911–928 (2009). https://doi.org/10.1007/s12220-009-9082-y
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DOI: https://doi.org/10.1007/s12220-009-9082-y