Holomorphic automorphisms of certain class of domains of infinite type. (English) Zbl 0817.32011

Kang, Hyeonbae

Tôhoku Math. J., II. Ser. 46, No. 3, 435-442 (1994).

This paper investigates the holomorphic automorphisms of a special kind of Hartogs’ domains in \(\mathbb{C}^ 2\): \[ E_ p = \bigl\{ (z_ 1, z_ 2) \in \mathbb{C}^ 2 : | z_ 1 |^ 2 + P(z_ 1, \overline z_ 2) < 1 \bigr\} \] where \(P\) is a subharmonic function with \(P(0) = 0\). These automorphisms form a group \(\operatorname{Aut} (E_ p)\), and its compactness is proved, if \(D\) is of infinite type, which means, at any point of the boundary \(\partial D\), the Levi form for \(D\) vanishes up to the infinite order in the complex tangential direction.

Reviewer: Na Jisheng (Beijing)

MSC:

32H02	Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
32T99	Pseudoconvex domains
32A07	Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32M05	Complex Lie groups, group actions on complex spaces

Keywords:

holomorphic automorphism; Hartog’s domain; domain of infinite type

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