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An Ahlfors Islands Theorem for non-archimedean meromorphic functions


Author: Robert L. Benedetto
Journal: Trans. Amer. Math. Soc. 360 (2008), 4099-4124
MSC (2000): Primary 30G06; Secondary 11J97, 12J25
DOI: https://doi.org/10.1090/S0002-9947-08-04546-7
Published electronically: March 11, 2008
MathSciNet review: 2395165
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Abstract: We present a $ p$-adic and non-archimedean version of Ahlfors' Five Islands Theorem for meromorphic functions, extending an earlier theorem of the author for holomorphic functions. In the non-archimedean setting, the theorem requires only four islands, with explicit constants. We present examples to show that the constants are sharp and that other hypotheses of the theorem cannot be removed.


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Additional Information

Robert L. Benedetto
Affiliation: Department of Mathematics and Computer Science, Amherst College, Amherst,Massachusetts 01002
Email: rlb@cs.amherst.edu

DOI: https://doi.org/10.1090/S0002-9947-08-04546-7
Keywords: $p$-adic analysis, Berkovich spaces, Ahlfors theory, covering surfaces
Received by editor(s): May 16, 2006
Published electronically: March 11, 2008
Additional Notes: The author gratefully acknowledges the support of a Miner D. Crary Research Fellowship from Amherst College
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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