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1 results

  • CONFORMAL SLIT MAPS IN APPLIED MATHEMATICS

  • Part of
  • DARREN CROWDY
  • Journal:
    The ANZIAM Journal / Volume 53 / Issue 3 / January 2012
    Published online by Cambridge University Press:
    17 September 2012, pp. 171-189
    • Article
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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.