Advertisement

Mathematische Annalen

, Volume 331, Issue 3, pp 693–711 | Cite as

Rational proper holomorphic maps from B n into B2 n

  • Hidetaka HamadaEmail author
Article

Abstract.

In this paper, we will investigate rational proper holomorphic maps from B n into B2 n , when n≥4.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alexander, H.: Proper holomorphic mappings in Cn. Indiana Univ. Math. J. 26, 137–146 (1977)Google Scholar
  2. 2.
    Chern, S.S., Moser, J.K.: Real hypersurfaces in complex manifolds. Acta Math. 133, 219–271 (1974)zbMATHGoogle Scholar
  3. 3.
    Cima, J., Suffridge, T.J.: A reflection principle with applications to proper holomorphic mappings. Math. Ann. 265, 489–500 (1983)Google Scholar
  4. 4.
    Cima, J., Suffridge, T.J.: Proper holomorphic mappings from the two-ball to the three-ball. Trans. Am. Math. Soc. 311, 227–239 (1989)Google Scholar
  5. 5.
    Cima, J., Suffridge, T.J.: Boundary behavior of rational proper maps. Duke Math. J. 60, 135–138 (1990)CrossRefGoogle Scholar
  6. 6.
    D’Angelo, J.P.: Proper holomorphic maps between balls of different dimensions. Mich. Math. J. 35, 83–90 (1988)CrossRefGoogle Scholar
  7. 7.
    Faran, J.: Maps from the two ball to the three ball. Invent. Math. 68, 441–475 (1982)Google Scholar
  8. 8.
    Faran, J.: The linearity of proper holomorphic maps between balls in the low codimensional case. J. Diff. Geom. 24, 15–17 (1986)Google Scholar
  9. 9.
    Forstneric, F.: Proper holomorphic maps from balls. Duke Math. J. 53, 427–441 (1986)CrossRefGoogle Scholar
  10. 10.
    Hamada, H.: Monomial proper maps between balls of different dimensions. Bull. Kyushu Kyoritsu Univ. Fac. Engineer. 15, 41–43 (1991)Google Scholar
  11. 11.
    Hamada, H.: On some proper holomorphic maps between balls of different dimensions. Proceedings of the First Korean-Japanese Colloquium on Finite or Infinite Dimensional Complex Analysis, 1993, pp. 77–82Google Scholar
  12. 12.
    Hamada, H.: Proper holomorphic mappings between balls which are linear on parallel hyperplanes. Bull. Kyushu Kyoritsu Univ. Fac. Engineer. 19, 7–13 (1995)Google Scholar
  13. 13.
    Huang, X.: On a linearity problem of proper holomorphic maps between balls in complex spaces of different dimensions. J. Diff. Geom. 51, 13–33 (1999)Google Scholar
  14. 14.
    Huang, X., Ji, S.: Mapping Bn into B2n-1. Invent. Math. 145, 219–250 (2001)CrossRefGoogle Scholar
  15. 15.
    Rudin, W.: Function theory in the unit ball of Cn. (Springer, New-York 1980)Google Scholar
  16. 16.
    Webster, S.: On mapping an n-ball into an (n+1)-ball in the complex space. Pac. J. Math. 81, 267–272 (1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Faculty of EngineeringKyushu Sangyo UniversityHigashi-kuJapan

Personalised recommendations