### Abstract

Sullivan showed that there exists K_{0} such that if Ω ⊂ ℂ is a simply connected hyperbolic domain, then there exists a conformally natural K_{0}-quasiconformal map from Ω to the boundary Dome(Ω) of the convex hull of its complement which extends to the identity on ∂Ω. Explicit upper and lower bounds on K_{0} were obtained by Epstein, Marden, Markovic and Bishop. We improve on these bounds, by showing that one may choose K_{0} ≤ 7.1695.

Original language | English (US) |
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Pages (from-to) | 146-168 |

Number of pages | 23 |

Journal | Proceedings of the London Mathematical Society |

Volume | 112 |

Issue number | 1 |

DOIs | |

State | Published - Feb 18 2015 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Bridgeman, M., Canary, R., & Yarmola, A. (2015). An improved bound for Sullivan's convex hull theorem.

*Proceedings of the London Mathematical Society*,*112*(1), 146-168. https://doi.org/10.1112/plms/pdv064