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Approximation of analytic functions with prescribed boundary conditions by circle packing maps

Tomasz Dubejko
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Abstract

We use recent advances in circle packing theory to develop a constructive method for the approximation of an analytic function $F:Ω\to \bold C$ by circle packing maps providing we have only been given $Ω$, $|F'|\big|_Ω$, 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.

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Tomasz Dubejko. 1995-01-25. Approximation of analytic functions with prescribed boundary conditions by circle packing maps. https://arxiv.org/abs/math/9501217

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