Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture
Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture
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 …