Three Remarks about the Carathéodory Distance

Marek Jarnicki and Peter Pflug
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Marek Jarnicki: Jagiellonian University, Institute of Mathematics
Peter Pflug: Universita̎t Osnabru̎ck, Abteilung Vechta, Mathematik

A chapter in Deformations of Mathematical Structures, 1989, pp 161-170 from Springer

Abstract: 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].

Keywords: Holomorphic Function; Unit Disc; Product Formula; Schwarz Lemma; Reinhardt Domain (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-94-009-2643-1_15

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