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Holomorphic Automorphism Groups of (m,1)-Circular Domains

  • Shuxia Feng
  • Hongjun LiEmail author
  • Chunhui Qiu
Article
  • 34 Downloads

Abstract

A quasi-circular domain of weight (mp) in \({\mathbb {C}}^2 \) is in fact a (mp)-circular domain Cartan (J Math Pures Appl 96:1–114, 1931). In this article, we give isotropic subgroups and holomorphic automorphism groups of bounded (m, 1)-circular domains under linear equivalences by Lie group technique. Adding to Thullen (Math Ann 104:244–259, 1931), Xu (Acta Math Sin 13(3):419–432, 1963), holomorphic automorphisms of bounded (mp)-circular domains are determined.

Keywords

Quasi-circular domain \((m{, }p)\)-circular domain Holomorphic automorphism group Isotropic subgroup 

Mathematics Subject Classification

32H02 

Notes

Acknowledgements

The authors would like to thank Prof. Daniel Zhuang-Dan Guan and Prof. Yichao Xu for giving us useful discussions. The authors are also pleased to thank the referees for very helpful comments and suggestions. This research is supported by the National Natural Science Foundation of China (Grant Nos. 11571288, 11771357).

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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHenan UniversityKaifengPeople’s Republic of China
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China

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