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Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture

Christopher J. Bishop Mathematics Department, State University of New York at Stony Brook

TBD mathscidoc:1701.332971

Arkiv for Matematik, 40, (1), 1-26, 2000.10
We show that proving the conjectured sharp constant in a theorem of Dennis Sullivan concerning convex sets in hyperbolic 3-space would imply the Brennan conjecture. We also prove that any conformal map$f$:$D$→Ω can be factored as a$K$-quasiconformal self-map of the disk (with$K$independent of Ω) and a map$g$:$D$→Ω with derivative bounded away from zero. In particular, there is always a Lipschitz homeomorphism from any simply connected Ω (with its internal path metric) to the unit disk.
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@inproceedings{christopher2000quasiconformal,
  title={Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture},
  author={Christopher J. Bishop},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203603237263780},
  booktitle={Arkiv for Matematik},
  volume={40},
  number={1},
  pages={1-26},
  year={2000},
}
Christopher J. Bishop. Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture. 2000. Vol. 40. In Arkiv for Matematik. pp.1-26. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203603237263780.
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