APPROXIMATION OF ANALYTIC

FUNCTIONS WITH PRESCRIBED BOUNDARY

CONDITIONS BY CIRCLE PACKING MAPS

Tomasz Dubejko

Abstract. We use recent advances in circle packing theory to develop a constructive method for the approximation of an analytic function F : Ω → C by circle packing maps providing we have only been given Ω, |F′||_{Ω}, and the set of critical points of F. This extends the earlier result of Ithiel Carter and Burt Rodin [CR] for F with no critical points.

Typeset by AMS-TEX