Advertisement

Chinese Annals of Mathematics, Series B

, Volume 39, Issue 4, pp 665–682 | Cite as

On Bounded Positive (m, p)-Circle Domains

  • Hongjun LiEmail author
  • Chunhui Qiu
  • Yichao Xu
Article

Abstract

Let D be a bounded positive (m, p)-circle domain in ℂ2. The authors prove that if dim(Iso(D)0) = 2, then D is holomorphically equivalent to a Reinhardt domain; if dim(Iso(D)0) = 4, then D is holomorphically equivalent to the unit ball in ℂ2. Moreover, the authors prove the Thullen’s classification on bounded Reinhardt domains in ℂ2 by the Lie group technique.

Keywords

(m, p)-Circular domain Reinhardt domain Holomorphically equivalent 

2000 MR Subject Classification

32A10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Cartan, H., Sur les groupes de transformations analytiques, Act. Sci. Ind., Hermann, Paris, 1935.zbMATHGoogle Scholar
  2. [2]
    Thullen, P., Zur den Abbildungen durch analytische Funktionen mehrerer komplexer Veränder-lichen, Math. Ann., 104, 1931, 244–259.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Cartan, H., Les fonctions de deux variables complexes et le problème de la représentation analytique, J. de Math., 10, 1931, 1–114.zbMATHGoogle Scholar
  4. [4]
    Cartan, H., Sur les transformations analytiques des domaines cerclés et semi-cerclés bornés, Math. Ann., 106, 1932, 540–573.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Xu, Y. C., On the holomorphic automorphism group of the bounded domain with positive (m, p) circle type, Acta Math. Sinica, 13, 1963, 419–432.(in Chinese).Google Scholar
  6. [6]
    Xu, Y. C. and Wang, D. L., On the classification of the bounded domains with semi-circle type in C2, Acta Math. Sinica, 23, 1980, 372–384.(in Chinese).MathSciNetGoogle Scholar
  7. [7]
    Yamamori, A., Automorphisms of normal quasi-circular domains, Bull. Sci. Math., 138, 2014, 406–415.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Yamamori, A., On the linearity of origin-preserving automorphisms of quasi-circular domains in Cn, J. Math. Anal. Appl., 426, 2015, 612–623.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Rong, F., On automorphisms of quasi-circular domains fixing the origin, Bull. Sci. Math., 140, 2016, 92–98.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Xu, Y. C., On the classification of symetric schlicht domains in several complex variable, Adv. Math., 8, 1965, 109–144 (in Chinese).Google Scholar

Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHenan UniversityKaifengChina
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenChina
  3. 3.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

Personalised recommendations