On the linearity of origin-preserving automorphisms of quasi-circular domains in ${\mathbb{C}}^n$

Abstract

A theorem due to Cartan asserts that every origin-preserving automorphism of bounded circular domains with respect to the origin is linear. In the present paper, by employing the theory of Bergman's representative domain, we prove that under certain circumstances Cartan's assertion remains true for quasi-circular domains in ${\mathbb{C}}^n$. Our main result is applied to obtain some simple criterions for the case $n=3$ and to prove that Braun-Kaup-Upmeier's theorem remains true for our class of quasi-circular domains.

12pages. To appear in Journal of Mathematical Analysis and Applications

References in corpus (4)

• Rigidity of proper holomorphic mappings between certain unbounded non-hyperbolic domains
• Automorphisms of normal quasi-circular domains
• Some estimates of the Bergman kernel of minimal bounded homogeneous domains
• On automorphisms of quasi-circular domains fixing the origin

Cited by in corpus (2)

• On biholomorphisms between bounded quasi-Reinhardt domains
• On automorphisms of quasi-circular domains fixing the origin