scholarly journals On the holomorphic automorphism group of a generalized Hartogs triangle

2016 ◽  
Vol 68 (1) ◽  
pp. 29-45 ◽  
Author(s):  
Akio Kodama
Keyword(s):  
Automorphism Group ◽  
Holomorphic Automorphism ◽  
Hartogs Triangle ◽  
Holomorphic Automorphism Group

On the holomorphic automorphism group of the Bergman–Hartogs domain

2015 ◽  
Vol 26 (08) ◽  
pp. 1550056 ◽  
Author(s):  
Jie Zhao ◽  
An Wang ◽  
Yihong Hao
Keyword(s):  
Automorphism Group ◽  
Large Class ◽  
Pseudoconvex Domains ◽  
Holomorphic Automorphism ◽  
Homogeneous Domain ◽  
Hartogs Domain ◽  
Holomorphic Automorphism Group

The Bergman–Hartogs domain which can be regarded as a generalization of the Cartan–Hartogs domain provides a large class of bounded pseudoconvex domains which are in general nonhomogeneous. Since the geometry of a domain is determined by its automorphism group to a certain extent, it is meaningful to study the structure of the automorphism group. In this paper, we completely determine the structure of the holomorphic automorphism group of the Bergman–Hartogs domain over a minimal homogeneous domain with center at the origin.

HOLOMORPHIC AUTOMORPHISMS AND PROPER HOLOMORPHIC SELF-MAPPINGS OF A TYPE OF GENERALISED MINIMAL BALL

2017 ◽  
Vol 96 (3) ◽  
pp. 455-467
Author(s):  
FENG RONG ◽  
BEN ZHANG
Keyword(s):  
Automorphism Group ◽  
Convex Domain ◽  
Holomorphic Automorphism ◽  
Holomorphic Automorphisms ◽  
Holomorphic Automorphism Group

In this paper, we first give a description of the holomorphic automorphism group of a convex domain which is a simple case of the so-called generalised minimal ball. As an application, we show that any proper holomorphic self-mapping on this type of domain is biholomorphic.

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