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

Part of: Holomorphic mappings and correspondences Holomorphic functions of several complex variables

Published online by Cambridge University Press:  18 August 2017

FENG RONG Open the ORCID record for FENG RONG [Opens in a new window]  and
BEN ZHANG
FENG RONG*
Affiliation:
Department of Mathematics, School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, PR China email frong@sjtu.edu.cn
BEN ZHANG
Affiliation:
Department of Mathematics, School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, PR China email alex_zhangben@sjtu.edu.cn
*
✉frong@sjtu.edu.cn
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Abstract

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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.

Keywords

holomorphic automorphismsproper holomorphic self-mappingsgeneralised minimal ball

MSC classification

Primary: 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
Secondary: 32H35: Proper mappings, finiteness theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 455 - 467
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

The authors are partially supported by the National Natural Science Foundation of China (Grant No. 11371246).

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