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A counterexample to Cartan's conjecture
on holomorphic curves omitting hyperplanes

Author: Alexandre Eremenko
Journal: Proc. Amer. Math. Soc. 124 (1996), 3097-3100
MSC (1991): Primary 30D45; Secondary 32H30
MathSciNet review: 1328347
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Abstract: In his 1928 thesis H. Cartan proved a theorem which can be considered as an extension of Montel's normality criterion to holomorphic curves in complex projective plane $\text {\bf P}^2$. He also conjectured that a similar result is true for holomorphic curves in $\text {\bf P}^n$ for any $n$. A counterexample to this conjecture is constructed for any $n\geq 3$.

References [Enhancements On Off] (What's this?)

  • 1. Lars V. Ahlfors, Lectures on Quasiconformal Mappings, D. Van Nostrand, Princeton, NJ 1966. MR 34:336
  • 2. Henri Cartan, Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, Ann. École Normale Supèr., 45 (1928), 255--346.
  • 3. Serge Lang, Introduction to Complex Hyperbolic Spaces, Springer-Verlag, NY, 1987. MR 88f:32065

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Additional Information

Alexandre Eremenko
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Received by editor(s): March 29, 1995
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society

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