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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
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 . He also conjectured that a similar result is true for holomorphic curves in for any . A counterexample to this conjecture is constructed for any .
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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