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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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

  • 1. Lars V. Ahlfors, Lectures on quasiconformal mappings, Manuscript prepared with the assistance of Clifford J. Earle, Jr. Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. MR 0200442 (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, New York, 1987. MR 886677 (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: http://dx.doi.org/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
Article copyright: © Copyright 1996 American Mathematical Society