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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 2, Pages 196–205 (Mi izv810)  

This article is cited in 10 scientific papers (total in 10 papers)

On orbit connectedness, orbit convexity and envelopes of holomorphy

Xiang-Yu Zhouab

a Steklov Math. Institute, Academy of Sciences, Moscow, Russian
b Institute of math., Academia Sinica, Beijing, P.R. China

Abstract: We are concerned with the univalence and discription of the envelope of holomorphy $E(D)$ for a domain $D$ having a compact Lie group action. Our main result is the following:
Let $X$ be a holomorphic Stein $K^C$-manifold, $D\subset X$ a $K$-invariant orbit connected domain. Then $E(D)$ is schlicht and orbit convex if and only if $E(K^C\cdot D)$ is schlicht. Moreover, in this case, $E(K^C\cdot D)=K^C\cdot e(d)$.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:2, 403–413

Bibliographic databases:

UDC: 517.55
MSC: 32D10, 32A07
Received: 18.01.1992
Language:

Citation: Xiang-Yu Zhou, “On orbit connectedness, orbit convexity and envelopes of holomorphy”, Izv. RAN. Ser. Mat., 58:2 (1994), 196–205; Russian Acad. Sci. Izv. Math., 44:2 (1995), 403–413

Citation in format AMSBIB
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\by Xiang-Yu Zhou
\paper On~orbit connectedness, orbit convexity and envelopes of holomorphy
\jour Izv. RAN. Ser. Mat.
\yr 1994
\vol 58
\issue 2
\pages 196--205
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\zmath{https://zbmath.org/?q=an:0835.32006}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44..403Z}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 2
\pages 403--413
\crossref{https://doi.org/10.1070/IM1995v044n02ABEH001604}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RB41200011}


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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. Zhou X., “On Invariant Domains in Certain Complex Homogeneous Spaces”, Ann. Inst. Fourier, 47:4 (1997), 1101–&  crossref  mathscinet  zmath  isi
    2. X.-Yu. Zhou, “A proof of the extended future tube conjecture”, Izv. Math., 62:1 (1998), 201–213  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Zhou X., “The Extended Future Tube Is a Domain of Holomorphy”, Math. Res. Lett., 5:1-2 (1998), 185–190  mathscinet  zmath  isi
    4. A. G. Sergeev, Xian-Yu Zhou, “Extended Future Tube Conjecture”, Proc. Steklov Inst. Math., 228 (2000), 25–42  mathnet  mathscinet  zmath
    5. Wu XiaoWen Deng FuSheng Zh.X., “Rigidity and Regularity in Group Actions”, Sci. China Ser. A-Math., 51:4 (2008), 819–826  crossref  mathscinet  zmath  isi
    6. Deng F., Zhou X., “Rigidity of Automorphism Groups of Invariant Domains in Certain Stein Homogeneous Manifolds”, C. R. Math., 350:7-8 (2012), 417–420  crossref  mathscinet  zmath  isi
    7. 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
    8. 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
    9. Ning J. Zhang H. Zhou X., “Proper holomorphic mappings between invariant domains in $\mathbb {C}^n$”, Trans. Am. Math. Soc., 369:1 (2017), 517–536  crossref  mathscinet  zmath  isi  scopus
    10. Xiangyu Zhou, “Recent Results in Several Complex Variables and Complex Geometry”, Proc. Steklov Inst. Math., 311 (2020), 245–260  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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