Christopher Green

Conformal Mappings to Multiply Connected Polycircular Arc Domains

There has been much recent interest in finding analytical formulae for conformal mappings from canonical multiply connected circular regions to multiply connected polygonal regions. Such formulae are the multiply connected generalizations of the Schwarz-Christoffel formula of classical function theory. A natural generalization of polygonal domains is the class of polycircular arc domains whose boundaries are a union of circular arc segments. This paper describes a theoretical method for the construction of conformal mappings from multiply connected circular domains, of arbitrary finite connectivity, to conformally equivalent polycircular arc domains. This work generalizes results on the doubly connected case by Crowdy & Fokas [10].