Conformal slit maps in applied mathematics

Darren Crowdy


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.



conformal slit maps, Schottky–Klein prime function, multiply connected.


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.