On quasiconformal equivalence of Schottky regions

Abstract

In a recent paper, H. Shiga proved that the regions of discontinuity of any two Schottky groups of ranks at least two are quasiconformally equivalent. In this paper, we provide an alternative proof of such a fact. Our approach permits us to discuss quasiconformality equivalence of regions of discontinuity of Schottky type groups in terms of their signatures.