On quasiconformal equivalence of Schottky regions
Rubén A. Hidalgo
Universidad de La Frontera, Temuco, Chile

Abstract
This paper concerns the general question: When are two homeomorphic Riemann surfaces quasiconformally equivalent? For the case of finite-type Riemann surfaces, the answer is known; it depends on the genus, the number of punctures, and the number of hyperbolic boundaries. On the other hand, for the case of infinite-type Riemann surfaces, this is rather complicated. We provide a general solution for those Riemann surfaces , where is a Cantor set being the limit set of a finitely generated Kleinian group. As a consequence, we obtain that there are four different Teichmüller spaces of Cantor limit sets of finitely generated Kleinian groups.
Cite this article
Rubén A. Hidalgo, On quasiconformal equivalence of Schottky regions. Groups Geom. Dyn. (2025), published online first
DOI 10.4171/GGD/926