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Three Remarks about the Carathéodory Distance

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Deformations of Mathematical Structures

Abstract

Let D be a domain in ℂn. The Carathéodory pseudodistance cD on D is defined by

$$ {c_D}(z',z'') = 1/2\log \frac{{1 + c_D^{*}(z',z'')}}{{1 - c_D^{*}(z',z'')}} $$

, where c *D denotes the Mo̎bius function

$$ c_D^{*}\left( {z',z''} \right) = \sup \left\{ {\left| {f\left( {z''} \right)} \right|:f:D \to E holomorphic,f\left( {z'} \right) = 0} \right\} $$

; here E is the unit disc in the complex plane. The Carathéodory pseudodistance is a very useful tool in complex analysis. For its standard properties we refer, for example, to the book by T. Frazoni-E. Vesentini [4].

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References

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Jagiellonian University, PL-30-059, Kraków, Poland

    Marek Jarnicki

  2. Abteilung Vechta, Mathematik, Universita̎t Osnabru̎ck, D-2848, Vechta 1, Deutschland

    Peter Pflug

Authors
  1. Marek Jarnicki
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  2. Peter Pflug
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Editors and Affiliations

  1. Institute of Mathematics of the Polish Academy of Sciences, Łódź, Poland

    Julian Ławrynowicz

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© 1989 Kluwer Academic Publishers

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Jarnicki, M., Pflug, P. (1989). Three Remarks about the Carathéodory Distance. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_15

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  • DOI: https://doi.org/10.1007/978-94-009-2643-1_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7693-7

  • Online ISBN: 978-94-009-2643-1

  • eBook Packages: Springer Book Archive

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