Proper holomorphic embeddings of finitely connected planar domains into ℂn

Abstract

In this paper we consider proper holomorphic embeddings of finitely connected planar domains into ℂⁿ that approximate given proper embeddings on smooth curves. As a side result we obtain a tool for approximating a $\mathcal{C}^{\infty}$ diffeomorphism on a polynomially convex set in ℂⁿ by an automorphism of ℂⁿ that satisfies some additional properties along a real embedded curve.