Conformal mapping in linear time

Given any $ε>0$ and any planar region $Ω$ bounded by a simple n-gon $P$ we construct a ($1 + ε)$-quasiconformal map between $Ω$ and the unit disk in time $C(ε)n$. One can take $C(ε) = C + C \log (1/ε) \log \log (1/ε)$.

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