On the boundary orbit accumulation set for a domain with non-compact automorphism group

1996/04/30 by A. V. Isaev, Isaev, A. V., S. G. Krantz +1
Mathematics · #32 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32

paper · pdf · doi:10.48550/arxiv.math/9604205

arxiv created 1996/06/04 · arxiv updated 2009/11/30

Abstract

For a smoothly bounded pseudoconvex domain D⊂\Bbb Cⁿ of finite type with non-compact holomorphic automorphism group Aut(D), we show that the set S(D) of all boundary accumulation points for Aut(D) is a compact subset of ∂ D and, if S(D) contains at least three points, it is connected and thus has the power of the continuum. We also discuss how S(D) relates to other invariant subsets of ∂ D and show in particular that S(D) is always a subset of the Šilov boundary.

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