Area and Hausdorff dimension of Sierpiski carpet Julia sets

We prove the existence of rational maps whose Julia sets are Sierpiski carpets having positive area. Such rational maps can be constructed such that they either contain a Cremer fixed point, a Siegel disk or are infinitely renormalizable. We also construct some Sierpiski carpet Julia sets with zero area but with Hausdorff dimension two. Moreover, for any given number s is an element of(1,2), we prove the existence of Sierpiski carpet Julia sets having Hausdorff dimension exactly s.