Automorphisms of normal quasi-circular domains

Abstract

It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal quasi-circular domains in ${\mathbb{C}}^2$ is linear.

10 pages. To appear in Bulletin des Sciences Mathematiques

Cited by in corpus (4)

• On biholomorphisms between bounded quasi-Reinhardt domains
• On the linearity of origin-preserving automorphisms of quasi-circular domains in ${\mathbb{C}}^n$
• On automorphisms of quasi-circular domains fixing the origin
• Unbounded Reinhardt domains with finite-dimensional Bergman spaces in $\C^n$