Examples of Domains with Non-Compact Automorphism Groups

{We give an example of a bounded, pseudoconvex, circular domain in ${\Bbb C}^n$ for any $n\ge 3$ with smooth real-analytic boundary and non-compact automorphism group, which is not biholomorphically equivalent to any Reinhardt domain. We also give an analogous example in ${\Bbb C}^2$, where the domain is bounded, non-pseudoconvex and such that the boundary is smooth real-analytic at all points except one and is $C^{1,\alpha}$-smooth at the exceptional point.}

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Published 1 January 1996