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Nov 9, 2017 at 10:18 vote accept Serguei Popov
Nov 9, 2017 at 5:15 comment added Alexandre Eremenko $\mathrm{cap}(A_r)$ must tend to $1$, the capacity of the unit disk, not to $0$ as $r\to 0$, as you wrote.
Nov 9, 2017 at 4:05 answer added Alexandre Eremenko timeline score: 8
Nov 8, 2017 at 22:03 comment added fedja Not sure about "useful", but it is definitely explicit: move $-1$ to $\infty$ by a fractional linear map and then shift the vertex of the resulting angle of aperture $3\pi/2$ to $0$ and apply $z^{2/3}$ to get a half-plane.
Nov 8, 2017 at 21:15 history asked Serguei Popov CC BY-SA 3.0