Inventiones mathematicae

, Volume 112, Issue 1, pp 323–349 | Cite as

Approximation of biholomorphic mappings by automorphisms of C n

  • Franc Forstnerič
  • Jean-Pierre Rosay


Biholomorphic Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abhyankar, S.S., Moh, T.T.: Embeddings of the line in the plane. J. Reine Angew. Math.,276, 148–166 (1975)Google Scholar
  2. 2.
    Alexander, H.: The polynomial hull of a rectifiable curve in Cn. Am. J. Math.110, 629–640 (1988)Google Scholar
  3. 3.
    Andersén, E.: Volume preserving automorphisms of Cn. Complex Variables14, 223–235 (1990)Google Scholar
  4. 4.
    Andersén, E., Lempert, L.: On the group of holomorphic automorphisms of Cn. Invent. Math.110, 371–388 (1992)Google Scholar
  5. 5.
    Bochner, S., Martin, W.T.: Several Complex Variables. Princeton: Princeton University Press 1948Google Scholar
  6. 6.
    Bony, J.-M.: Principle du maximum, inegalité de Harnack... Ann. Inst. Fourier19, 277–304 (1969)Google Scholar
  7. 7.
    Chirka, E.M.: Complex Analytic Sets (Math. Appl. vol 46) Dordrecht: Kluwer 1989; Original in Russian, Moskva: Nauka 1985Google Scholar
  8. 8.
    Dixon, P.G., Esterle, J.: Michael's problem and the Poincaré-Fatou-Bieberbach phenomenon. Bull. Amer. Math. Soc., New. Ser.15, 127–187 (1986)Google Scholar
  9. 9.
    Kallin, E.: Polynomial convexity: the three spheres problem. In: Aeppli, A. et al. (eds.) Proc. Conf. Complex Analysis, Minneapolis 1964, pp. 301–304. Berlin Heidelberg New York: Springer 1965Google Scholar
  10. 10.
    El Kasimi, A.: Approximation polynômiale dans les domaines étoilés de Cn. Complex Variables10, 179–182 (1988)Google Scholar
  11. 11.
    Forstneric, F.: Stability of polynomial convexity of totally real sets. Proc. Am. Math. Soc.96, 489–494 (1986)Google Scholar
  12. 12.
    Golubitsky, M., Guillemin, V.: Stable Mappings and Their Singularities. (Grad. Texts Math., vol. 14) Berlin Heidelberg New York: Springer 1973Google Scholar
  13. 13.
    Hirsch, M.: Differential Topology. (Grad. Texts Math., vol. 33) Berlin Heidelberg New York: Springer 1976Google Scholar
  14. 14.
    Hörmander, L.: An Introduction to Complex Analysis in Several Variables, 3rd ed. Amsterdam: North Holland 1990Google Scholar
  15. 15.
    Rosay, J.-P.: The polynomial hull of non-connected tube domains, and an example of E. Kallin. Bull. Lond. Math. Soc.21, 73–78 (1989)Google Scholar
  16. 16.
    Rosay, J.-P.: Straightening of arcs. (Preprint 1992)Google Scholar
  17. 17.
    Rosay, J.-P., Rudin, W.: Holomorphic maps from Cn to Cn. Trans. Am. Math. Soc.310, 47–86 (1988)Google Scholar
  18. 18.
    Rosay, J.-P., Rudin, W.: Holomorphic embeddings of C in Cn. In: Proc. Inst. Mittag-Leffler. Djursholm, 1987–88. Princeton: Princeton University Press 1993Google Scholar
  19. 19.
    Steenrod, N.: The Topology of Fibre Bundles. Princeton: Princeton University Press 1951Google Scholar
  20. 20.
    Stolzenberg, G.: Polynomially and rationally convex sets. Acta Math.109, 259–289 (1963)Google Scholar
  21. 21.
    Stout, E.L.: The Theory of Uniform Algebras. Tarrytown on Hudson: Bogden and Quigley 1971Google Scholar
  22. 22.
    Wells, R.O.: Compact real submanifolds of a complex manifold with nondegenerate holomorphic tangent bundles. Math. Ann.179, 123–129 (1969)Google Scholar
  23. 23.
    Wermer, J.: The hull of a curve in Cn. Ann. Math.68, 550–561 (1958)Google Scholar
  24. 24.
    Wermer, J.: Banach Algebras and Several Complex Variables. Berlin Heidelberg New York: Springer 1976Google Scholar
  25. 25.
    Forstneric, F.: Complements of Runge domains and polynomial hulls. Michigan Math J. (to appear)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Franc Forstnerič
    • 1
  • Jean-Pierre Rosay
    • 1
  1. 1.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations