Uniformization of SierpiA"ski carpets in the plane

Let S-i, i is an element of I, be a countable collection of Jordan curves in the extended complex plane (C) over cap that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uniformly relatively separated, then there exists a quasiconformal map f : (C) over cap -> (C) over cap such that f (S-i) is a round circle for all i is an element of I. This implies that every Sierpinski carpet in (C) over cap whose peripheral circles are uniformly relatively separated uniform quasicircles can be mapped to a round Sierpinski carpet by a quasisymmetric map.