On the quasiconformal equivalence of dynamical Cantor sets

Abstract

The complement of a Cantor set in the complex plane is itself regarded as a Riemann surface of infinite type. The problem of this paper is the quasiconformal equivalence of such Riemann surfaces. Particularly, we are interested in Riemann surfaces given by Cantor sets which are created through dynamical methods. discuss the quasiconformal equivalence for the complements of Cantor Julia sets of rational functions and generalized Cantor sets. We also consider the Teichmüller distance between generalized Cantor sets.