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2004 Types of complete infinitely sheeted planes
Mitsuru Nakai
Nagoya Math. J. 176: 181-195 (2004).


We will answer negatively to the question whether the completeness of infinitely sheeted covering surfaces of the extended complex plane have anything to do with their types being parabolic or hyperbolic. This will be accomplished by giving a one parameter family $\{ W[\alpha] : \alpha \in {\cal A} \}$ of complete infinitely sheeted planes $W[\alpha]$ depending on the parameter set ${\cal A}$ of sequences $\alpha = (a_{n})_{n \geq 1}$ of real numbers $0 < a_{n} \leq 1/2$ $(n \geq 1)$ such that $W[\alpha]$ is parabolic for 'small' $\alpha$'s and hyperbolic for 'large' $\alpha$'s.


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Mitsuru Nakai. "Types of complete infinitely sheeted planes." Nagoya Math. J. 176 181 - 195, 2004.


Published: 2004
First available in Project Euclid: 27 April 2005

zbMATH: 1084.30049
MathSciNet: MR2108127

Primary: 30F20
Secondary: 30C25 , 30C35 , 30F25

Rights: Copyright © 2004 Editorial Board, Nagoya Mathematical Journal

Vol.176 • 2004
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