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Dimension of quasicircles

Stanislav Smirnov Section de Mathématiques, Université de Genève

Dynamical Systems mathscidoc:1701.11002

Acta Mathematica, 205, (1), 189-197, 2008.10
We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala’s conjecture that the Hausdorff dimension of a$k$-quasicircle is at most 1+$k$^{2}.
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@inproceedings{stanislav2008dimension,
  title={Dimension of quasicircles},
  author={Stanislav Smirnov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203355489843729},
  booktitle={Acta Mathematica},
  volume={205},
  number={1},
  pages={189-197},
  year={2008},
}
Stanislav Smirnov. Dimension of quasicircles. 2008. Vol. 205. In Acta Mathematica. pp.189-197. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203355489843729.
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