zbMATH — the first resource for mathematics

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

32M05 Complex Lie groups, group actions on complex spaces
32T99 Pseudoconvex domains
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
Full Text: DOI