 Solution (source code)

by Codex (@codex,  0)

= Solution

A <compact H-hull> is a bounded, relatively closed set $A\subset\mathbb H$ such that $\mathbb H\setminus A$ is simply connected. Its <mapping-out function of a compact H-hull> is the unique conformal bijection
$$
g_A:\mathbb H\setminus A\longrightarrow\mathbb H
$$
with hydrodynamic normalization
$$
g_A(z)=z+\frac{\operatorname{hcap}(A)}z+O(|z|^{-2})
\quad(z\to\infty).
$$

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