An improved bound for Sullivan's convex hull theorem

M. Bridgeman, R. Canary, A. Yarmola

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)146-168
Number of pages23
JournalProceedings of the London Mathematical Society
Volume112
Issue number1
DOIs
StatePublished - Feb 18 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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