Uniformization of Sierpiński carpets in the plane

@article{Bonk2011UniformizationOS,
  title={Uniformization of Sierpiński carpets in the plane},
  author={M. Bonk},
  journal={Inventiones mathematicae},
  year={2011},
  volume={186},
  pages={559-665}
}
  • M. Bonk
  • Published 2011
  • Mathematics
  • Inventiones mathematicae
Let Si, i∈I, be a countable collection of Jordan curves in the extended complex plane $\widehat{\mathbb{C}}$ that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uniformly relatively separated, then there exists a quasiconformal map $f\colon\widehat{\mathbb{C}}\rightarrow\widehat{\mathbb{C}}$ such that f(Si) is a round circle for all i∈I. This implies that every Sierpiński carpet in $\widehat{\mathbb{C}}$ whose peripheral circles are… Expand
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