Mathematische Annalen

, Volume 305, Issue 1, pp 559–569 | Cite as

Embedding holomorphic discs through discrete sets

  • Franc Forstneric
  • Josip Globevnik
  • Berit Stensønes
Article

Mathematics Subject Classification (1991)

32H02 32H35 32M05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abraham, R., Marsden, J.E.: Foundations of Mechanics, 2nd. ed. Reading: Benjamin 1987Google Scholar
  2. 2.
    Alexander, H.: The polynomial hull of a rectifiable curve inC n. Amer. J. Math.110, 629–640 (1988)Google Scholar
  3. 3.
    Andersén, E.: Volume-preserving automorphisms ofC n. Complex Variables14, 223–235 (1990)Google Scholar
  4. 4.
    Andersén, E., Lempert, L.: On the group of holomorphic automorphisms ofC n. Inventiones Math.110, 371–388 (1992)Google Scholar
  5. 5.
    Forstneric, F.: Approximation by automorphisms on smooth submanifolds ofC n. Math. Ann.300, 719–738 (1994)Google Scholar
  6. 6.
    Forstneric, F., Globevnik, J.: Discs in pseudoconvex domains. Comment. Math. Helvetici67, 129–145 (1992)Google Scholar
  7. 7.
    Forstneric, F., Globevnik, J., Rosay, J.-P.: Non straightenable complex lines inC 2. Preprint, April 1995Google Scholar
  8. 8.
    Forstneric, F., Rosay, J.-P.: Approximation of biholomorphic mappings by automorphisms ofC n. Invent. Math.112, 323–349 (1993). Correction, Invent. Math.118, 573–574 (1994)Google Scholar
  9. 9.
    Globevnik, J.: Relative embeddings of discs into convex domains. Invent. Math.98, 331–350 (1989)Google Scholar
  10. 10.
    Globevnik, J., Stensønes, B.: Holomorphic embeddings of planar domains intoC 2. Math. Ann. (1995)Google Scholar
  11. 11.
    Hörmander, L., Wermer, J.: Uniform approximation on compact sets inC n. Math. Scand.23, 5–21 (1968)Google Scholar
  12. 12.
    Hörmander, L.: An Introduction to Complex Analysis in Several Variables, 3rd ed. Amsterdam: North Holland 1990Google Scholar
  13. 13.
    Range, R.M. and Siu, Y.T.:C k approximation by holomorphic functions and\(\bar \partial \) forms onC k submanifolds of a complex manifold. Math. Ann.210, 105–122 (1974)Google Scholar
  14. 14.
    Rosay, J.-P.: Straightening of arcs. (Colloque d'analyse complexe et géométrie, Marseille, 1992, pp. 217–226). Astérisque217, 1993Google Scholar
  15. 15.
    Rosay, J.-P., Rudin, W.: Holomorphic maps fromC n toC n. Trans. Amer. Math. Soc.310, 47–86 (1988)Google Scholar
  16. 16.
    Rosay, J.-P., Rudin, W.: Holomorphic embeddings ofC inC n. In Several complex variables: Proceedings of the Mittag Leffler Institute, 1987–88, J.E. Fornaess Ed., 563–569, Math. Notes38, Princeton Univ. Press (1993)Google Scholar
  17. 17.
    Stolzenberg, G.: Polynomially and rationally convex sets. Acta Math.109, 259–289 (1963)Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Franc Forstneric
    • 1
  • Josip Globevnik
    • 2
  • Berit Stensønes
    • 3
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Institute of MathematicsPhysics and MechanicsLjubljanaSlovenia
  3. 3.Department of MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations