Uniformization of a Once-Punctured Annulus

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• 作者：Tanran Zhang (1) (2)
  
  1. Department of Mathematics ; Soochow University ; No.1 Shizi Street ; Suzhou ; 215006 ; China
  2. Division of Mathematics ; Graduate School of Information Sciences ; Tohoku University ; 6-3-09 Aramaki-Aza-Aoba ; Aoba-ku ; Sendai ; 980-8579 ; Japan
  
• 关键词：Uniformization ; Hyperbolic metric ; Punctured annulus ; Collar ; Extremal length ; 30F10 ; 14Q05
• 刊名：Computational Methods and Function Theory
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：15
• 期：1
• 页码：75-91
• 全文大小：445 KB
• 参考文献：1. Anderson, GD, Vamanamurthy, MK, Vuorinen, M (1997) Conformal Invariants, Inequalities, and Quasiconformal Maps. Wiley, New York
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• 刊物主题：Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable;
• 出版者：Springer Berlin Heidelberg
• ISSN：2195-3724

文摘

The universal cover or the covering group of a hyperbolic Riemann surface \(X\) is important but hard to express explicitly. It can be, however, detected by the uniformization and a suitable description of \(X\) . 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 \(A\) in terms of five parameter pairs and give explicit formulas about the hyperbolic structure and the complex structure of \(A\) . Several degenerate cases are also treated.