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I wonder weather an explicit conformal map of a sinus-shaped region given by $\Re(z) \in [0, 1+\delta \sin(\Im(z)) ]$ onto say a strip or a ball is known (of course $0<\delta < 1$). Thank you.

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    $\begingroup$ Explicit conformal maps can almost never be given; why would you expect one here? The answer is highly likely to be "no", but good estimates can be given about the behaviour of the conformal map if required. $\endgroup$
    – Lasse Rempe
    Commented Apr 27, 2016 at 16:24

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