Generalization of a theorem of Clunie and Hayman
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- by Matthew Barrett and Alexandre Eremenko
- Proc. Amer. Math. Soc. 140 (2012), 1397-1402
- DOI: https://doi.org/10.1090/S0002-9939-2011-11033-5
- Published electronically: August 10, 2011
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Abstract:
Clunie and Hayman proved that if the spherical derivative $\| f’\|$ of an entire function satisfies $\| f’\|(z)=O(|z|^\sigma )$, 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.References
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Bibliographic 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
- MR Author ID: 63860
- Email: eremenko@math.purdue.edu
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2869124