Generalization of a theorem of Clunie and Hayman

TL;DR

This paper extends a classical theorem relating the growth of the spherical derivative of entire functions to the order of the functions, generalizing it to holomorphic curves in projective space avoiding hyperplanes.

Contribution

The paper generalizes Clunie and Hayman's theorem from entire functions to holomorphic curves in projective space, establishing new growth bounds.

Findings

Extended the theorem to holomorphic curves in projective space

Established bounds on the order of growth for these curves

Generalized classical results to higher-dimensional complex analysis

Abstract

Clunie and Hayman proved that if the spherical derivative of an entire function has order of growth sigma then the function itself has order at most sigma+1. We extend this result to holomorphic curves in projective space of dimension n omitting n hyperplanes in general position.