Nearly closed semicircular slit
= Nearly closed semicircular slit
{title2=$K_L=m^{-1}(i(0,L])$}
With $m(z)=(z+1)/(1-z)$, the <compact H-hull> $K_L=m^{-1}(i(0,L])$ is a unit semicircular arc attached at $-1$, with a narrow passage near $1$. As $L\to\infty$, its normalized <mapping-out function of a compact H-hull> tends to $2$ at each fixed point of the interior bay. Points in that bay tending to $-1$ therefore have displacement approaching three. The order of these two limits is important.