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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 1175–1184 | Cite as

A Note on Envelopes of Holomorphy

  • Marek JarnickiEmail author
  • Peter Pflug
Article
  • 161 Downloads

Abstract

Let p:XM be a Riemann domain over a connected n-dimensional complex submanifold M of \(\mathbb{C}^{N}\) and let \(\mathcal{F}\subset \mathcal{O}(X)\) be such that \(p\in\mathcal{F}^{N}\). Our aim is to discuss relations between the \(\mathcal{F}\)-envelope of holomorphy of (X,p) in the sense of Riemann domains over M and the \(\mathcal{F}\)-envelope of holomorphy of X in the sense of complex manifolds.

Keywords

Riemann domain Envelope of holomorphy 

Mathematics Subject Classification (2010)

32D10 32D15 32D25 

Notes

Acknowledgements

The authors thank the referee for his precise proposals which improved the paper.

References

  1. 1.
    Fornæss, J.-E., Zame, W.R.: Riemann domains and envelopes of holomorphy. Duke Math. J. 50, 273–283 (1983) CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Grauert, H.: Charakterisierung der holomorph vollständigen komplexen Räume. Math. Ann. 129, 233–259 (1955) CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Gunning, R., Rossi, H.: Analytic Functions of Several Complex Variables. Prentice Hall, Englewood Cliffs (1965) zbMATHGoogle Scholar
  4. 4.
    Jarnicki, M., Pflug, P.: Extension of Holomorphic Functions. De Gruyter Expositions in Mathematics, vol. 34. Walter de Gruyter, Berlin (2000) CrossRefzbMATHGoogle Scholar
  5. 5.
    Kerner, H.: Holomorphiehüllen zu K-vollständigen komplexen Räumen. Math. Ann. 138, 316–328 (1959) CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Rossi, H.: On envelopes of holomorphy. Commun. Pure Appl. Math. 16, 9–17 (1963) CrossRefzbMATHGoogle Scholar
  7. 7.
    Vigué, J.-P.: Construction d’enveloppes d’holomorphie par la méthode de H. Cartan et P. Thullen. Math. Ann. 259, 111–118 (1982) CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer Science, Institute of MathematicsJagiellonian UniversityKrakówPoland
  2. 2.Institut für MathematikCarl von Ossietzky Universität OldenburgOldenburgGermany

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