Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Next Article Computational Methods and Function Theory 5 (2005), No. 1, 159--184 Copyright Heldermann Verlag 2005 On Schwarz's Lemma in Multiply Connected Domains Gerald Schmieder schmieder@mathematik.uni-oldenburg.de , Fakultät V, Institut für Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany. [Abstract-pdf] [Abstract-ps] Let $G$ be a $n$-connected domain in the complex plane and let $z_0\in G$ be fixed. We consider the class $H_1(G,z_0)$ of all holomorphic functions~$f$ of $G$ into the unit disk $E$ with $f(z_0)=0$. For $z\in G\setminus\{z_0\}$ the Carath\'eodory distance $c(z,z_0)$ is defined as the maximum of $|f(z)|$, $f\in H_1(G,z_0)$. We determine explicitely the balls \$\{z\in G:\, c(z,z_0) Keywords: Carathéodory distance, ring domains, extremal functions. MSC 2000: 30C75, 30C80. [FullText-pdf (372 K)] [FullText-ps (649 K)]