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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 4, Pages 866–873 (Mi izv1539)  

This article is cited in 7 scientific papers (total in 7 papers)

The hartogs phenomenon for holomorphically convex Kähler manifolds

S. M. Ivashkovich


Abstract: It is said that the Hartogs phenomenon occurs for a complex manifold $Y$ if every holomorphic mapping $f$ of a domain $D$ over $\mathbf C^n$ into $Y$ extends to a holomorphic mapping $\widetilde f$ of the envelope of holomorphy $\widetilde D$ into $Y$. In this paper it is proved that a holomorphically convex Kähler manifold $Y$ exhibits the Hartogs phenomenon if and only if $Y$ contains no rational curves.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:1, 225–232

Bibliographic databases:

UDC: 517.5
MSC: 32D10
Received: 27.01.1986

Citation: S. M. Ivashkovich, “The hartogs phenomenon for holomorphically convex Kähler manifolds”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 866–873; Math. USSR-Izv., 29:1 (1987), 225–232

Citation in format AMSBIB
\Bibitem{Iva86}
\by S.~M.~Ivashkovich
\paper The hartogs phenomenon for holomorphically convex K\"ahler manifolds
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 4
\pages 866--873
\mathnet{http://mi.mathnet.ru/izv1539}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=864181}
\zmath{https://zbmath.org/?q=an:0618.32011}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 1
\pages 225--232
\crossref{https://doi.org/10.1070/IM1987v029n01ABEH000968}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. M. Ivashkovitch, “Spherical shells as obstructions for the extension of holomorphic mappings”, J Geom Anal, 2:4 (1992), 351  crossref  elib
    2. O ALEHYANE, “Une extension du théorème de Hartogs pour les applications séparément holomorphes”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 324:2 (1997), 149  crossref
    3. DO DUC THAI, NGUYEN THI TUYET MAI, “HARTOGS-TYPE EXTENSION THEOREMS FOR SEPARATELY HOLOMORPHIC MAPPINGS ON COMPACT SETS”, Int. J. Math, 11:05 (2000), 723  crossref
    4. Viêt-Anh Nguyên, Peter Pflug, “Cross Theorems with Singularities”, J Geom Anal, 2009  crossref  isi
    5. Benjamin McKay, “Extension Phenomena for Holomorphic Geometric Structures”, SIGMA, 5 (2009), 058, 45 pp.  mathnet  crossref  mathscinet
    6. Viet-Anh Nguyen, “Recent Developments in the Theory of Separately Holomorphic Mappings”, Colloquium Mathematicum, 117:2 (2009), 175–206  crossref  isi
    7. F. Neji, “Equicontinuous families of meromorphic mappings with values in compact complex surfaces”, Complex Variables and Elliptic Equations, 2011, 1  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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