Advertisement

On Runge Neighborhoods of Closures of Domains Biholomorphic to a Ball

  • Hervé Gaussier
  • Cezar Joiţa
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 26)

Abstract

We give an example of a domain W in \(\mathbb {C}^3\), biholomorphic to a ball, such that W is not Runge in any Stein neighborhood of \( \overline {W}\).

Keywords

Approximation of univalent maps Runge domain Fatou-Bieberbach domains 

Mathematics Subject Classification

32E30 30E10 

Notes

Acknowledgements

The article was discussed during the conference “Geometric Function Theory in Higher Dimension” held in Cortona, September 2016. The authors would like to thank the organizers for their invitation. The authors would also like to thank the referee for his useful comments. The author Hervé Gaussier was partially supported by ERC ALKAGE. The author Cezar Joiţa was partially supported by CNCS grant PN-III-P4-ID-PCE-2016-0330.

References

  1. 1.
    Hörmander, L.: An Introduction to Complex Analysis in Several Variables. D. Van Nostrand, Princeton, NJ (1966)zbMATHGoogle Scholar
  2. 2.
    Wermer, J.: An example concerning polynomial convexity. Math. Ann. 139, 147–150 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Wermer, J.: Addendum to “An example concerning polynomial convexity”. Math. Ann. 140, 322–323 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Wermer, J.: On a domain equivalent to the bidisk. Math. Ann. 248, 193–194 (1980)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.University of Grenoble AlpesCNRSGrenobleFrance
  2. 2.Simion Stoilow Institute of Mathematics of the Romanian AcademyBucharestRomania

Personalised recommendations