  For Cantor circle Julia sets of hyperbolic rational maps, we prove that they
are quasisymmetrically equivalent to standard Cantor circles (i.e., connected
components are round circles). This gives a quasisymmetric uniformization of
all Cantor circle Julia sets of hyperbolic rational maps.
  By analyzing the combinatorial information of the rational maps whose Julia
sets are Cantor circles, we give a computational formula of the number of the
Cantor circle hyperbolic components in the moduli space of rational maps for
any fixed degree.
  We calculate the Hausdorff dimensions of the Julia sets which are Cantor
circles, and prove that for any Cantor circle hyperbolic component
$\mathcal{H}$ in the space of rational maps, the infimum of the Hausdorff
dimensions of the Julia sets of the maps in $\mathcal{H}$ is equal to the
conformal dimension of the Julia set of any representative $f_0\in\mathcal{H}$,
and that the supremum of the Hausdorff dimensions is equal to $2$.
