Dimension and Measures for a Curvilinear Sierpinski Gasket or Apollonian Packing

Abstract

In this paper we apply some results about general conformal iterated function systems toA, the residual set of a standard Apollonian packing or a curvilinear Sierpinski gasket. Within this context, it is straightforward to show thath, the Hausdorff dimension ofA, is greater than 1 and the packing dimension and the upper and lower box counting dimensions are all the same as the Hausdorff dimension. Among other things, we verify Sullivan's result that 0