Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T01:25:24.074Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on quasi-Reinhardt domains

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

Published online by Cambridge University Press:  27 December 2018

Fengbai Li  and
Feng Rong
Fengbai Li
Affiliation:
Department of Applied Mathematics, School of Mathematics, Shanghai University of Finance and Economics, 777 Guo Ding Road, Shanghai 200433, P.R. China ([email protected])
Feng Rong
Affiliation:
Department of Mathematics, School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, P.R. China ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We present some fundamental properties of quasi-Reinhardt domains, in connection with Kobayashi hyperbolicity, minimal domains and representative domains. We also study proper holomorphic correspondences between quasi-Reinhardt domains.

Keywords

quasi-Reinhardt domainminimal domainrepresentative domainKobayashi hyperbolicBergman kernelproper holomorphic correspondence

MSC classification

Primary: 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
Secondary: 32A25: Integral representations; canonical kernels (Szegő, Bergman, etc.) 32H99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 2 , April 2019 , pp. 297 - 304
Copyright
Copyright © Royal Society of Edinburgh 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bell, S.. The Bergman kernel function and proper holomorphic mappings. Trans. Amer. Math. Soc. 270 (1982), 685–691.Google Scholar
2Bell, S.. Proper holomorphic correspondences between circular domains. Math. Ann. 270 (1985), 393–400.Google Scholar
3Bell, S.. Algebraic mappings of circular domains in Cn. In Several Complex Variables (Stockholm, 1987/1988), Math. Notes, vol. 38, Fornaess, John Erik (ed), pp. 126–135 (Princeton, NJ: Princeton Univ. Press, 1993).Google Scholar
4Bergman, S.. The kernel function and conformal mapping, 2nd edn, Mathematical Surveys no. V (Providence, RI, Amer. Math. Soc., 1970).Google Scholar
5Bochner, S. and Martin, W.. Several Complex Variables (Princeton, N.J.: Princeton Univ. Press, 1948).Google Scholar
6Bröcker, T. and Dieck, T.. Representations of Compact Lie Groups. In Grad. Texts in Math., vol. 98 (New York: Springer-Verlag, 1985).Google Scholar
7Deng, F. and Rong, F.. On biholomorphisms between bounded quasi-Reinhardt domains. Ann. Mat. Pura Appl. 195 (2016), 835–843.Google Scholar
8Greene, R., Kim, K.-T. and Krantz, S.. The Geometry of Complex Domains. In Prog. in Math., vol. 219 (Boston: Birkhäuser, 2011).Google Scholar
9Heinzner, P.. On the automorphisms of special domains in Cn. Indiana Univ. Math. J. 41, (1992), 707–712.Google Scholar
10Kobayashi, S.. Hyperbolic Manifolds and Holomorphic Mappings, 2nd edn (Singapore: World Sci. Publ. Co. Pte. Ltd., 2005).Google Scholar
11Kodama, A.. Boundedness of circular domains. Proc. Japan Acad., Ser. A Math. Sci. 58 (1982), 227–230.Google Scholar
12Lu, Q.-K.. On the representative domain. In Several Complex Variables, Hangzhou, 1981 (Boston, MA: Birkhäuser Basel, 1984), pp. 199–211.Google Scholar
13Maschler, M.. Minimal domains and their Bergman kernel function. Pacific J. Math. 6 (1956), 501–516.Google Scholar
14Rong, F.. On automorphisms of quasi-circular domains fixing the origin. Bull. Sci. Math. 140 (2016), 92–98.Google Scholar
15Stein, K.. Topics on holomorphic correspondences. Rocky Mountain J. Math. 2 (1972), 443–463.Google Scholar
16Tsuboi, T.. Bergman representative domains and minimal domains. Japan. J. Math. 29 (1959), 141–148.Google Scholar