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Uniformization of a Once-Punctured Annulus

Uniformization of a Once-Punctured Annulus The universal cover or the covering group of a hyperbolic Riemann surface $$X$$ X is important but hard to express explicitly. It can be, however, detected by the uniformization and a suitable description of $$X$$ X . Beardon proposed five different ways to describe twice-punctured disks using fundamental domain, hyperbolic length, collar and extremal length in 2012. We parameterize a once-punctured annulus $$A$$ A in terms of five parameter pairs and give explicit formulas about the hyperbolic structure and the complex structure of $$A$$ A . Several degenerate cases are also treated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Uniformization of a Once-Punctured Annulus

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0095-6
Publisher site
See Article on Publisher Site

Abstract

The universal cover or the covering group of a hyperbolic Riemann surface $$X$$ X is important but hard to express explicitly. It can be, however, detected by the uniformization and a suitable description of $$X$$ X . Beardon proposed five different ways to describe twice-punctured disks using fundamental domain, hyperbolic length, collar and extremal length in 2012. We parameterize a once-punctured annulus $$A$$ A in terms of five parameter pairs and give explicit formulas about the hyperbolic structure and the complex structure of $$A$$ A . Several degenerate cases are also treated.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Nov 4, 2014

References