Abstract
We show that proving the conjectured sharp constant in a theorem of Dennis Sullivan concerning convex sets in hyperbolic 3-space would imply the Brennan conjecture. We also prove that any conformal map f: D→Ω can be factored as a K-quasiconformal self-map of the disk (withK independent of Ω) and a map g: D→Ω with derivative bounded away from zero. In particular, there is always a Lipschitz homeomorphism from any simply connected Ω (with its internal path metric) to the unit disk.
Funding Statement
The author is partially supported by NSF Grant DMS 9800924.
Citation
Christopher J. Bishop. "Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture." Ark. Mat. 40 (1) 1 - 26, April 2002. https://doi.org/10.1007/BF02384499
Information