A counterexample to Cartan’s conjecture on holomorphic curves omitting hyperplanes
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- by Alexandre Eremenko PDF
- Proc. Amer. Math. Soc. 124 (1996), 3097-3100 Request permission
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 $\mathbf {P}^2$. He also conjectured that a similar result is true for holomorphic curves in $\mathbf {P}^n$ for any $n$. A counterexample to this conjecture is constructed for any $n\geq 3$.References
- Lars V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. Manuscript prepared with the assistance of Clifford J. Earle, Jr. MR 0200442
- Henri Cartan, Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, Ann. École Normale Supèr., 45 (1928), 255–346.
- Serge Lang, Introduction to complex hyperbolic spaces, Springer-Verlag, New York, 1987. MR 886677, DOI 10.1007/978-1-4757-1945-1
Additional Information
- Alexandre Eremenko
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 63860
- Email: eremenko@math.purdue.edu
- Received by editor(s): March 29, 1995
- Communicated by: Albert Baernstein II
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3097-3100
- MSC (1991): Primary 30D45; Secondary 32H30
- DOI: https://doi.org/10.1090/S0002-9939-96-03392-8
- MathSciNet review: 1328347