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)|
|Number of pages||23|
|Journal||Proceedings of the London Mathematical Society|
|State||Published - Feb 18 2015|
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