Conformal slit maps in applied mathematics

Darren Crowdy

Abstract


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.

doi:10.1017/S1446181112000119

Keywords


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



DOI: http://dx.doi.org/10.21914/anziamj.v53i0.5782



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.