  It is well-known that the Julia set J(f) of a rational map is uniformly
perfect; that is, every ring domain which separates J(f) has bounded modulus,
with the bound depending only on f. In this article we prove that an analogous
result is true in higher dimensions; namely, that the Julia set J(f) of a
uniformly quasiregular mapping f in R^n is uniformly perfect. In particular,
this implies that the Julia set of a uniformly quasiregular mapping has
positive Hausdorff dimension.
