Computing Conformal Maps onto Circular Domains
نویسندگان
چکیده
We show that, given a non-degenerate, finitely connected domain D, its boundary, and the number of its boundary components, it is possible to compute a conformal mapping of D onto a circular domain without prior knowledge of the circular domain. We do so by computing a suitable bound on the error in the Koebe construction (but, again, without knowing the circular domain in advance). Recent results on the distortion of capacity by Thurman [25] and the computation of capacity by Ransford and Rostand [24] are used. As a scientifically sound model of computation with continuous data, we use an informal version of Type-Two Effectivity as developed by Kreitz and Weihrauch [27].
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