Computational Methods and Function Theory 1 (2001), No. 1, 155--163
Copyright Heldermann Verlag 2001
Martin Chuaqui
mchuaqui@mat.puc.cl, Facultad de Matematicas, P. Universidad Catolica de Chile, Casilla 306, Santiago 22, Chile.
Christian Pommerenke
pommeren@math.tu-berlin.de, Technische Universität Berlin, Fachbereich Mathematik, 10623 Berlin, Germany.
Let $f$ be a conformal map of the unit disk $\mathbb{D}$ onto a domain bounded by a curve $C$, which is of class $C^{3,\delta}$, except for a finite number of corners. In this paper we derive a representation formula of the Schwarzian derivative $Sf$, expressed in terms of the integral of the arclength derivative of the curvature of $C$ and a sum of polar terms corresponding to the vertices.
Keywords: Schwarzian derivative, curvature, smooth curve, corners.
MSC 2000: Primary 30E20, Secondary 30C20, 30C35.
[FullText-pdf (180 K)] [FullText-ps (236 K)]