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Automorphism groups of certain domains in $${\mathbb{C}}^ n$$ with a singular boundary. (English) Zbl 0698.32016
This paper demonstrates how to use the so-called scaling method in Several Complex Variables together with the theory of the set of singular boundary points to compute the automorphism groups of certain circular domains with non-smooth boundaries. As a concrete example, it is shown that the automorphism group of the Hahn-Pflug ball $$\{(z_ 1,...,z_ n):$$ $$| z_ 1|^ 2+...+| z_ n|^ 2+| z^ 2_ 1+...+z^ 2_ n| <2\},$$ where $$n\geq 2$$, is in fact $$\{e^{\sqrt{- 1}\theta}A|$$ $$\theta\in {\mathbb{R}}$$, $$A\in O(n,{\mathbb{R}})\}$$, where $${\mathbb{R}}$$ denotes the set of real numbers and where O(n,$${\mathbb{R}})$$ as usual the set of all $$n\times n$$ orthogonal matrices of real numbers.
Reviewer: K.-T.Kim

##### MSC:
 32M05 Complex Lie groups, group actions on complex spaces 32T99 Pseudoconvex domains 32A07 Special domains in $${\mathbb C}^n$$ (Reinhardt, Hartogs, circular, tube) (MSC2010)
##### Keywords:
pseudoconvex domains; automorphism groups; circular domains
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