Annales Academię Scientiarum Fennicę

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
**P**^{n} 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

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