Annales Academić Scientiarum Fennicć
Mathematica
Volumen 35, 2010, 565-570

BRODY CURVES OMITTING HYPERPLANES

Alexandre Eremenko

Purdue University, Department of Mathematics
West Lafayette, IN 47907-2067, U.S.A.; eremenko 'at' math.purdue.edu

Abstract. A Brody curve, a.k.a. normal curve, is a holomorphic map f from the complex line C to the complex projective space Pⁿ such that the family of its translations {z \mapsto f(z + a) : a \in C} is normal. We prove that Brody curves omitting n hyperplanes in general position have growth order at most one, normal type. This generalizes a result of Clunie and Hayman who proved it for n = 1.

2000 Mathematics Subject Classification: Primary 32Q99, 30D15.

Key words: Holomorphic curve, spherical derivative.

Reference to this article: A. Eremenko: Brody curves omitting hyperplanes. Ann. Acad. Sci. Fenn. Math. 35 (2010), 565-570.

Full document as PDF file

doi:10.5186/aasfm.2010.3534