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Estimates for the hyperbolic metric of the punctured plane and applications

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Abstract

The hyperbolic metrich Ω of the twice punctured complex plane Ω is studied. A new recursive algorithm for computing the density λΩ ofh Ω is given. For a proper subdomainG of Ω we answer a question of G. Martin concerning quasiconformal mappings ofG that can be extended to the complement ofG as the identity map.

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Authors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, Fontanka 27, 191011, St. Petersburg, Russia

    A. Yu. Solynin

  2. Department of Mathematics, University of Helsinki, P.O. Box 4, FIN-00014, Yliopistonkatu 5, Finland

    M. Vuorinen

Authors
  1. A. Yu. Solynin
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  2. M. Vuorinen
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Correspondence to A. Yu. Solynin.

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Solynin, A.Y., Vuorinen, M. Estimates for the hyperbolic metric of the punctured plane and applications. Isr. J. Math. 124, 29–60 (2001). https://doi.org/10.1007/BF02772606

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  • DOI: https://doi.org/10.1007/BF02772606

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