One example of the boundary behaviour of biholomorphic transformations

Abstract

Two biholomorphically equivalent domains Ω 1 {\Omega _1} , Ω 2 ⊂ C 2 {\Omega _2} \subset {{\mathbf {C}}^2} with piecewise smooth boundaries and with the following property are constructed. If F : Ω 1 → Ω 2 F:{\Omega _1} \to {\Omega _2} is any biholomorphic transformation then neither F F nor F − 1 {F^{ - 1}} can be extended continuously to the boundary.