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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 1, Pages 16–40 (Mi izv1166)  

This article is cited in 21 scientific papers (total in 21 papers)

Holomorphic automorphisms of hyperbolic Reinhardt domains

N. G. Kruzhilin


Abstract: The author describes the group of holomorphic automorphisms of a Reinhardt domain in $\mathbf C^n$ that is a hyperbolic complex manifold. Explicit formulas are presented from which it can be seen, in particular, that hyperbolic Reinhardt domains that do not intersect the coordinate hyperplanes only have automorphisms of a very simple form.
Bibliography: 12 titles.

Full text: PDF file (3322 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 32:1, 15–38

Bibliographic databases:

UDC: 517.5
MSC: Primary 32A07, 32M05; Secondary 22E10, 32H99, 32C25, 57R30, 57R25
Received: 21.05.1986

Citation: N. G. Kruzhilin, “Holomorphic automorphisms of hyperbolic Reinhardt domains”, Izv. Akad. Nauk SSSR Ser. Mat., 52:1 (1988), 16–40; Math. USSR-Izv., 32:1 (1989), 15–38

Citation in format AMSBIB
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\by N.~G.~Kruzhilin
\paper Holomorphic automorphisms of hyperbolic Reinhardt domains
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 1
\pages 16--40
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=936521}
\zmath{https://zbmath.org/?q=an:0663.32019|0638.32024}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 32
\issue 1
\pages 15--38
\crossref{https://doi.org/10.1070/IM1989v032n01ABEH000732}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Anosov, “Flows on closed surfaces and behavior of trajectories lifted to the universal covering plane”, J Dyn Control Syst, 1:1 (1995), 125  crossref  mathscinet  zmath  elib
    2. A. V. Isaev, “Kähler-Einstein metric on Reinhardt domains”, J Geom Anal, 5:2 (1995), 237  crossref
    3. S. Aranson, E. Zhuzhoma, “Qualitative theory of flows on surfaces (A review)”, Journal of Mathematical Sciences (New York), 90:3 (1998), 2051  crossref  mathscinet  zmath
    4. A.V. Isaev, S.G. Krantz, “Domains with Non-Compact Automorphism Group: A Survey”, Advances in Mathematics, 146:1 (1999), 1  crossref
    5. P. A. Soldatkin, “Holomorphic equivalence of Reinhardt domains in $\mathbb C^2$”, Izv. Math., 66:6 (2002), 1271–1304  mathnet  crossref  crossref  mathscinet  zmath
    6. Akio Kodama, Satoru Shimizu, Journal of the Korean Mathematical Society, 40:3 (2003), 563  crossref
    7. N. G. Kruzhilin, P. A. Soldatkin, “Affine and Holomorphic Equivalence of Tube Domains in $\mathbb C^2$”, Math. Notes, 75:5 (2004), 623–634  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Kang-Tae Kim, Luigi Verdiani, “Complexn-dimensional manifolds with a realn 2-dimensional automorphism group”, J Geom Anal, 14:4 (2004), 701  crossref
    9. A. V. Isaev, “Characterization of the unit ball in C n among complex manifolds of dimensionn”, J Geom Anal, 14:4 (2004), 697  crossref
    10. N. G. Kruzhilin, P. A. Soldatkin, “Holomorphic Equivalence of Tube Domains in $\mathbb C^2$”, Proc. Steklov Inst. Math., 253 (2006), 90–99  mathnet  crossref  mathscinet  elib
    11. Proc. Steklov Inst. Math., 253 (2006), 225–245  mathnet  crossref  mathscinet
    12. Isaev A.V., Kruzhilin N.G., “Proper holomorphic maps between reinhardt domains in C-2”, Michigan Mathematical Journal, 54:1 (2006), 33–63  crossref  isi
    13. A. V. Isaev, “A Remark on a Theorem by Kodama and Shimizu”, J Geom Anal, 18:3 (2008), 795  crossref  mathscinet  zmath  isi
    14. Wu XiaoWen, Deng FuSheng, Zhou XiangYu, “Rigidity and Regularity in Group Actions”, Sci. China Ser. A-Math., 51:4 (2008), 819–826  crossref  mathscinet  zmath  isi
    15. Łukasz Kosiński, “Serre Problem for Unbounded Pseudoconvex Reinhardt Domains in ℂ2 ”, J Geom Anal, 2010  crossref
    16. Fusheng Deng, Xiangyu Zhou, “Rigidity of automorphism groups of invariant domains in certain Stein homogeneous manifolds”, Comptes Rendus Mathematique, 2012  crossref
    17. F. Deng, Zhou Xiang Yu, “Rigidity of automorphism groups of invariant domains in homogeneous Stein spaces”, Izv. Math., 78:1 (2014), 34–58  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. A. G. Sergeev, Xiangyu Zhou, “Invariant domains of holomorphy: Twenty years later”, Proc. Steklov Inst. Math., 285 (2014), 241–250  mathnet  crossref  crossref  isi  elib  elib
    19. A. V. Isaev, “Proper actions of high-dimensional groups on complex manifolds”, Bull. Math. Sci, 2015  crossref
    20. S. Pinchuk, R. Shafikov, A. Sukhov, “Some Aspects of Holomorphic Mappings: A Survey”, Proc. Steklov Inst. Math., 298 (2017), 212–247  mathnet  crossref  crossref  isi  elib
    21. N. G. Kruzhilin, “Proper holomorphic maps of bounded two-dimensional Reinhardt domains. I”, Izv. Math., 85:3 (2021), 388–406  mathnet  crossref  crossref  isi  elib
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