Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

A REMARK ON GENERALIZED COMPLEX ELLIPSOIDS WITH SPHERICAL BOUNDARY POINTS

  • Kodama, Akio (Department of Mathematics Faculty of Science Kanazawa University)
  • Published : 2000.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

It is well-known that there is no analogue to the Riemann mapping theorem in the higher dimensional case. Therefore, it would be an interesting question to find sufficient conditionsl for domains to be biholomorphically equivalent to the unit bal. In this paper, we investigate this questionin the case where the given domains are generalized complex ellipsoids with spherical boundary points.

Keywords

References

  1. Math. Ann. v.209 Holomorphic mappings from the ball and polydisc H. Alexander
  2. J. Geom. Anal. v.7 Localization principle of automorphisms on generalized pseudoellipsoids G. Dini and A.;Selvaggi Primicerio
  3. Seminari di Geometria 1994-1995 Localization principle for a class of Reinhardt domains G. Dini;A. Selvaggi Primicerio
  4. Differential Geometry, Lie Groups, and Symmetric Spaces S. Helgason
  5. Math. Res. Lett. v.5 Global holomorphic extension of a local map and a Riemann mapping theorem for algebraic domains X. Huang;S. Ji.
  6. Tohoku Math. J. v.51 A characterization of certain weakly pseudoconvex domains A. Kodama
  7. Indiana Univ. Math. J. v.41 A characterization of generalized complex ellipsoids in Cⁿ and related results A. Kodama, S. G. Krantz;D. Ma
  8. Several complex variables R. Narasimhan
  9. Publ. Res. Inst. Math. Sci. v.4 The holomorphic equivalence problem for a class of Reinhardt domains I. Naruki
  10. Math. USSR Sb. v.27 On the analytic continuation of holomorphic mappings S. I. Pinchuk.
  11. Several Complex Variables III Holomorphic maps in Cⁿ and the problem of holomorphic equivalence Encyclopaedia of Math. Sciences S. I. Pinchuk;G. M. Khenkin(ed.)
  12. Function Theory in the Unit Ball of Cⁿ W. Rudin
  13. Several Complex Variables III v.9 The geometry of CR-manifolds, Encyclopaedia ences A. E. Tumanov;G. M. Khenkin(ed.)