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On automorphism groups of generalized Hua domains

Published online by Cambridge University Press:  19 February 2014

FENG RONG
FENG RONG*
Affiliation:
Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, P.R. China. e-mail: [email protected]
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Abstract

Hua domains, generalized Hua domains and Hua constructions, named after the great Chinese mathematician Luogeng Hua (Loo-Keng Hua), are generalizations of Cartan–Hartogs domains introduced by Weiping Yin around the end of the 20th century. In this paper, we give a complete description of automorphism groups of generalized Hua domains. We also discuss the corresponding problem for Hua constructions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 3 , May 2014 , pp. 461 - 472
Copyright
Copyright © Cambridge Philosophical Society 2014 

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References

REFERENCES

[1]Ahn, H., Byun, J. and Park, J.-D.Automorphisms of the Hartogs type domains over classical symmetric domains. Internat. J. Math. 23 (2012), 1250098 (11 pages).CrossRefGoogle Scholar
[2]Bedford, E. and Dadok, J.Bounded domains with prescribed group of automorphisms. Comment. Math. Helv. 62 (1987), 561–572.CrossRefGoogle Scholar
[3]Bedford, E. and Pinchuk, S.Domains in C2 with noncompact groups of holomorphic automorphisms (translated from Russian), Math. USSR-Sb. 63 (1989), 141–151.CrossRefGoogle Scholar
[4]Faraut, J., Kaneyuki, S., Korányi, A. and Lu, Q., Roos, G.Analysis and geometry on complex homogeneous domains. Progr. Math. 185 (Birkhäuser, 1999), 425–534.Google Scholar
[5]Greene, R., Kim, K.-T. and Krantz, S.The geometry of complex domains. Progr. Math. 219 (Birkhäuser, 2011).CrossRefGoogle Scholar
[6]Greene, R. and Krantz, S. Invariants of Bergman geometry and results concerning the automorphism groups of domains in Cn. Proceedings of the 1989 Conference in Cetraro (D. Struppa, ed.) (1991).Google Scholar
[7]Helgason, S.Differential Geometry, Lie Groups and Symmetric Spaces (Academic Press, Inc., 1978).Google Scholar
[8]Hua, L.Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains. Transl. Math. Monog. 6 (Amer. Math. Soc., Providence, RI, 1979).Google Scholar
[9]Kobayashi, S.Transformation Groups in Differential Geometry (Springer-Verlag, New York-Heidelberg, 1972).CrossRefGoogle Scholar
[10]Krantz, S.Function Theory of Several Complex Variables. (Amer. Math. Soc., Providence, RI, 2000).Google Scholar
[11]Narasimhan, R.Several Complex Variables. Chicago Lectures in Math. (Chicago University Press, Chicago-London, 1971).Google Scholar
[12]Rosay, J.-P.Sur une caractérisation de la boule parmi les domaines de Cn par son groupe d' automorphismes. Ann. Inst. Fourier (Grenoble) 29 (1979), 91–97.CrossRefGoogle Scholar
[13]Saerens, R. and Zame, W.The isometry groups of manifolds and the automorphism groups of domains. Trans. Amer. Math. Soc. 301 (1987), 413–429.CrossRefGoogle Scholar
[14]Wang, A., Yin, W., Zhang, L. and Roos, G.The Kähler-Einstein metric for some Hartogs domains over symmetric domains. Sci. China Ser. A: Math. 49 (2006), 1175–1210.CrossRefGoogle Scholar
[15]Wong, B.Characterization of the unit ball in Cn by its automorphism group. Invent. Math. 41 (1977), 253–257.CrossRefGoogle Scholar
[16]Yin, W.Lu Qi–Keng conjecture and Hua domain. Sci. China Ser. A: Math. 51 (2008), 803–818.CrossRefGoogle Scholar