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An Integral Representation Formula of the Schwarzian Derivative

An Integral Representation Formula of the Schwarzian Derivative Let f be a conformal map of the unit disk D onto a domain bounded by a curve C, which is of class C 3,δ, except for a finite number of corners. In this paper we derive a representation formula of the Schwarzian derivative S f, 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

An Integral Representation Formula of the Schwarzian Derivative

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Publisher
Springer Journals
Copyright
Copyright © 2001 by Heldermann Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03320982
Publisher site
See Article on Publisher Site

Abstract

Let f be a conformal map of the unit disk D onto a domain bounded by a curve C, which is of class C 3,δ, except for a finite number of corners. In this paper we derive a representation formula of the Schwarzian derivative S f, 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.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References