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›› 2013, Vol. 30 ›› Issue (2): 156-158.DOI: 10.7523/j.issn.1002-1175.2013.02.002

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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 Online:2013-03-15
  • Supported by:

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

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

CLC Number: