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A multi-point Schwarz-Pick Lemma

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Abstract

We state and prove a general version of the Schwarz-Pick Lemma that involves more than two points in the hyperbolic plane and with appears to contain all known variations of the classical result. We give some applications to complex function theory and then discuss our result in the context of the Pick-Nevanlinna Theorem.

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Authors and Affiliations

  1. Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CB3 0WB, Cambridge, England

    A. F. Beardon

  2. Department of Mathematical Sciences, University of Cincinnati, 45221, Cincinnati, OH, USA

    D. Minda

Authors
  1. A. F. Beardon
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  2. D. Minda
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Beardon, A.F., Minda, D. A multi-point Schwarz-Pick Lemma. J. Anal. Math. 92, 81–104 (2004). https://doi.org/10.1007/BF02787757

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  • DOI: https://doi.org/10.1007/BF02787757

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