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
$$
g_A(z)=z+\frac{\operatorname{hcap}(A)}z+O(|z|^{-2})
\quad(z\to\infty).
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 203 / 1 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-203/1/a/solution