Multiply Connected Quadrature Domains and the Bergman Kernel Function

This paper derives general analytical formulae for the conformal maps from multiply connected circular preimage domains to multiply connected quadrature domains by considering the Bergman kernel functions of the preimage and target domains. The new formulae are expressed in terms of the Schottky–Klein prime function. They generalize, to the case of arbitrary connectivity, a formula relevant to doubly connected domains derived by Y. Avci in 1977. Submitted: September 17, 2007. Accepted: June 5, 2008.