An improved bound for Sullivan's convex hull theorem

M. Bridgeman; R. Canary; A. Yarmola

doi:10.1112/plms/pdv064

An improved bound for Sullivan's convex hull theorem

M. Bridgeman
, R. Canary
, A. Yarmola

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Sullivan showed that there exists K₀ such that if Ω ⊂ ℂ is a simply connected hyperbolic domain, then there exists a conformally natural K₀-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 K₀ were obtained by Epstein, Marden, Markovic and Bishop. We improve on these bounds, by showing that one may choose K₀ ≤ 7.1695.

Original language	English (US)
Pages (from-to)	146-168
Number of pages	23
Journal	Proceedings of the London Mathematical Society
Volume	112
Issue number	1
DOIs	https://doi.org/10.1112/plms/pdv064
State	Published - Feb 18 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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AB - Sullivan showed that there exists K0 such that if Ω ⊂ ℂ is a simply connected hyperbolic domain, then there exists a conformally natural K0-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 K0 were obtained by Epstein, Marden, Markovic and Bishop. We improve on these bounds, by showing that one may choose K0 ≤ 7.1695.

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An improved bound for Sullivan's convex hull theorem

Abstract

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