On biholomorphisms between bounded quasi-Reinhardt domains

Abstract

In this paper, we define what is called a quasi-Reinhardt domain and study biholomorphisms between such domains. We show that all biholomorphisms between two bounded quasi-Reinhardt domains fixing the origin are polynomial mappings, and we give a uniform upper bound for the degree of such polynomial mappings. In particular, we generalize the classical Cartan's linearity theorem for circular domains to quasi-Reinhardt domains.

9 pages

References in corpus (2)

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

Cited by in corpus (1)

• On the degree of automorphisms of quasi-circular domains fixing the origin