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中国科学院大学学报 ›› 2013, Vol. 30 ›› Issue (2): 156-158.DOI: 10.7523/j.issn.1002-1175.2013.02.002

• 数学 • 上一篇    下一篇

关于C-{0,1}上Poincaré度量边界估计的一个简单方法

邓富声1, 刘伟明2   

  1. 1. 中国科学院研究生院数学科学学院, 北京 100049;
    2. 北京石油化工学院数理系, 北京 102617
  • 收稿日期:2011-12-28 修回日期:2012-05-02 发布日期:2013-03-15
  • 通讯作者: LIU Wei-Ming
  • 基金资助:

    Supported by NSFC(11001148, 10826073, 10901161), President Fund of GUCAS, and BJJW(Z2011-008)

A simple method for the boundary estimate of Poincaré metric on C-{0,1}*

DENG Fu-Sheng1, LIU Wei-Ming2   

  1. 1. School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China;
    2. Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China
  • Received:2011-12-28 Revised:2012-05-02 Published:2013-03-15
  • Supported by:

    Supported by NSFC(11001148, 10826073, 10901161), President Fund of GUCAS, and BJJW(Z2011-008)

摘要:

给出 C-{0,1}上Poincaré度量边界估计的一个新方法.该方法简单、直接,不涉及Ahlfors关于超双曲度量的Schwarz引理,也不涉及调和分析和模函数的内容.

关键词: 覆盖映射, 双曲区域, Poincaré, 度量, Schwarz-Pick引理, 边界估计

Abstract:

We give a boundary estimate of Poincaré metric on C-{0, 1} using a simple direct method, which does not involve Ahlfors's Schwarz lemma about ultrahyperbolic metrics, harmonic analysis, or modular functions.

Key words: covering maps, hyperbolic domains, Poincaré, metric, Schwarz-Pick lemma, boundary estimate

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