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On a problem of Bremermann concerning Runge domains

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Abstract

In this paper we give an example of a bounded Stein domain in \(\mathbb{C}^{n}\), with smooth boundary, which is not Runge and whose intersection with every complex line is simply connected.

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References

  1. Andersson M., Passare M., Sigurdsson R. (2004) Complex convexity and analytic functionals. Progress in Mathematics, vol. 225. Birkhäuser Verlag, Basel

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  2. Bremermann H.J. (1958) Die Charakterisierung Rungescher Gebiete durch plurisubharmonische Funktionen. Math. Ann. 136, 173–186

    Article  MATH  MathSciNet  Google Scholar 

  3. Fornæss J.E., Stensønes B. (1987) Lectures on Counterexamples in Several Complex Variables. Mathematical Notes, vol. 33. Princeton University Press Princeton

  4. Hörmander L. (1994) Notions of convexity. Progress in Mathematics, vol. 127. Birkhäuser Basel

  5. Ohsawa, T.: Analysis of several complex variables. Translations of Mathematical Monographs, vol. 211. American Mathematical Society (2002)

  6. Wermer J. (1959) An example concerning polynomial convexity. Math. Ann. 139, 147–150

    Article  MathSciNet  Google Scholar 

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Correspondence to Cezar Joiţa.

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This work was supported by Marie Curie International Reintegration Grant no. 013023 and by the Romanian Ministry of Education and Research grant 2-CEx06-11-10/25.07.06.

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Joiţa, C. On a problem of Bremermann concerning Runge domains. Math. Ann. 337, 395–400 (2007). https://doi.org/10.1007/s00208-006-0041-7

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  • DOI: https://doi.org/10.1007/s00208-006-0041-7

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