Half-plane capacity of a vertical slit
= Half-plane capacity of a vertical slit
{title2=$\operatorname{hcap}((x,x+ih])=h^2/2$}
For a vertical slit of height $h>0$ attached at $x\in\mathbb R$, the <mapping-out function of a compact H-hull> is $g(z)=x+\sqrt{(z-x)^2+h^2}$, with the branch asymptotic to $z-x$ at infinity. Its <half-plane capacity> is $h^2/2$.