An improved bound for Sullivan's convex hull theorem

作者：Bridgeman M^*; Canary R^*; Yarmola A^*

来源：Proceedings of the London Mathematical Society, 2016, 112(1): 146-168.

DOI：10.1112/plms/pdv064

Sullivan showed that there exists K-0 such that if Omega subset of (C) over cap is a simply connected hyperbolic domain, then there exists a conformally natural K-0-quasiconformal map from Omega to the boundary Dome(Omega) of the convex hull of its complement which extends to the identity on partial derivative Omega. 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.

• 出版日期2016-1