Conformal Mapping of Doubly Connected Regions

Abstract

Let be the unit disk, and let G be a doubly connected region bounded by the unit circle and a Jordan curve . We defined [9] a point system on C be an extremal property, which turned out to be very efficient to approximate the conformal mapping f of onto G. Here we show that is equally distributed on . If C is an analytic Jordan curve. Further, we show how to apply this point system to conformal mappings not only for regions of type G, but also to the case that the doubly connected region is bounded by two Jordan curves. As an example, we numerically approximate the conformai mapping of an annulus onto a doubly connected region bounded by “concentric squares”.