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Generalization of a theorem of Clunie and Hayman


Authors: Matthew Barrett and Alexandre Eremenko
Journal: Proc. Amer. Math. Soc. 140 (2012), 1397-1402
MSC (2010): Primary 32Q99, 30D15
DOI: https://doi.org/10.1090/S0002-9939-2011-11033-5
Published electronically: August 10, 2011
MathSciNet review: 2869124
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Abstract: Clunie and Hayman proved that if the spherical derivative $ \Vert f'\Vert$ of an entire function satisfies $ \Vert f'\Vert(z)=O(\vert z\vert^\sigma)$, then $ T(r,f)=O(r^{\sigma+1}).$ We generalize this to holomorphic curves in projective space of dimension $ n$ omitting $ n$ hyperplanes in general position.


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Additional Information

Matthew Barrett
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Alexandre Eremenko
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: eremenko@math.purdue.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11033-5
Received by editor(s): November 17, 2010
Received by editor(s) in revised form: January 6, 2011
Published electronically: August 10, 2011
Additional Notes: The first and second authors are supported by NSF grant DMS-0555279
The second author is also supported by the Humboldt Foundation
Communicated by: Mario Bonk
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.