The Beltrami equation and ring homeomorphisms

Abstract

With the aid of results by Gehring, we introduce and study plane ring Q-homeomorphisms. This study is then applied in deriving general principles on the existence and uniqueness of homeomorphic ACL solutions to the Beltrami equation extending earlier results. In particular, we obtain new existence criteria which are expressed in terms of finite mean oscillation majorants for tangential dilatations. Moreover, we give a new proof of our generalization of the well-known Lehto existence theorem that has, in turn, a number of other consequences.