Solution
= Solution
A <compact H-hull> is a bounded relatively closed set $A\subset\mathbb H$ for which $\mathbb H\setminus A$ is a <simply connected domain>. Its <mapping-out function of a compact H-hull> is the unique <conformal map> $g_A:\mathbb H\setminus A\to\mathbb H$ with <hydrodynamic normalization at infinity>
$$
g_A(z)=z+\frac{a}{z}+O(|z|^{-2}).
$$
Its <half-plane capacity> is $\operatorname{hcap}(A)=a$.