Examples of domains with non-compact automorphism groups

1996/02/09 by Siqi Fu, Alexander Isaev, A. V. Isaev +4
Mathematics · #32 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32

paper · pdf · doi:10.48550/arxiv.math/9602201

arxiv created 1996/02/09 · openalex publication_date 1996/02/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give, in dimensions three or greater, an example of a bounded, pseudoconvex, circular domain in complex space with smooth real analytic boundary and non-compact automorphism group which is not biholomorphically equivalent to any Reinhardt domain. We give an analogous example in dimension two, but the domain fails to be smooth at one boundary point---indeed it is not in any Lipschitz class at the exceptional point.

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