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 (with$K$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.