Teichmuller density, holomorphic motions and forgetful mappings

In my joint work with Frederick Gardiner we study the fibers of forgetful mappings between Teichmuller spaces. Holomorphic motions provide a way to describe these fibers. The inherited Teichmuuler density on the fibers
induces a density that is equivalent to Poincare density. Estimating this density we find interesting applications to uniformly perfect sets, Poincare Theta series and Teichmuller spaces.