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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

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

Author(s): Alexandre Eremenko
Journal: Proc. Amer. Math. Soc. 124 (1996), 3097-3100.
MSC (1991): Primary 30D45; Secondary 32H30
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Abstract | References | Similar articles | Additional information

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:

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
Email: eremenko@math.purdue.edu

DOI: 10.1090/S0002-9939-96-03392-8
PII: S 0002-9939(96)03392-8
Received by editor(s): March 29, 1995
Communicated by: Albert Baernstein II
Copyright of article: Copyright 1996, American Mathematical Society


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