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CONFORMAL SLIT MAPS IN APPLIED MATHEMATICS

Part of: Geometric function theory

Published online by Cambridge University Press:  17 September 2012

DARREN CROWDY
DARREN CROWDY*
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK (email: [email protected])
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Abstract

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Conformal slit maps play a fundamental theoretical role in analytic function theory and potential theory. A lesser-known fact is that they also have a key role to play in applied mathematics. This review article discusses several canonical conformal slit maps for multiply connected domains and gives explicit formulae for them in terms of a classical special function known as the Schottky–Klein prime function associated with a circular preimage domain. It is shown, by a series of examples, that these slit mapping functions can be used as basic building blocks to construct more complicated functions relevant to a variety of applied mathematical problems.

Keywords

conformal slit mapsSchottky–Klein prime functionmultiply connected

MSC classification

Secondary: 30C20: Conformal mappings of special domains
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 3 , January 2012 , pp. 171 - 189
Copyright
Copyright © Australian Mathematical Society 2012

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