Factorization of proper holomorphic mappings through Thullen domains

Abstract

Given a bounded domain in C-2 and a proper holomorphic mapping onto the unit ball in C-2, we give a criterion for a proper mapping to factor through Thullen domains by its branch locus. As an application, we present a characterization of the Thullen domains among bounded domains admitting a proper holomorphic mapping onto the unit ball.