Spirals and the Asymptotic Teichmüller Space

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• 作者：Hideki Miyachi
• 关键词：Jordan domains ; Teichmüller space ; Asymptotic Teichmüller space ; Bers embedding ; Quasiarcs ; Primary 30F60 ; Secondary 30C20 ; 32G15 ; 30C62 ; 30C65
• 刊名：Computational Methods and Function Theory
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：14
• 期：2-3
• 页码：609-622
• 全文大小：327 KB
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  14. Osgood, B.: Old and New on the Schwarzian derivative, Quasiconformal Mappings and Analysis, A Collection of Papers Honoring F.W.Gehring. pp. 275-08 (1998)
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  16. Thurston, W.: Zippers and univalent functions. In: (The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of the Proof), Mathematical Surveys Monographs, vol. 21, pp. 185-97. American Mathematical Society, Providence (1986)
  
• 作者单位：Hideki Miyachi (1)
  
  1. Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka?, 560-0043, Japan
  
• ISSN：2195-3724

文摘

In this paper, we will study the Bers density problem for the asymptotic Teichmüller space of the unit disk. We first observe that Gehring’s spiral domain is asymptotically equivalent to a Jordan domain in the closure of the universal Teichmüller space. We will also show that the asymptotic class of Flinn’s domain is not in the closure of the asymptotic Teichmüller space. This answers in the negative the Bers density problem for the asymptotic Teichmüller space.