Conformal mapping of long quadrilaterals and thick doubly connected domains

In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to “long quadrilaterals,” i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of the rectangle to the four corners of the quadrilateral.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41340/1/365_2005_Article_BF01303524.pd