An explicit holomorphic map of bounded domains in \({\mathbb{C}}^ n\) with \(C^ 2\)-boundary onto the polydisc (Q797730)

By theorems of Fornaess and Stout, every n-dimensional connected paracompact complex manifold M is the image of a regular, finitely fibered holomorphic map from the ball \(B_ n\) or the polydisc \(\Delta_ n\) in \({\mathbb{C}}^ n\). In this paper it is shown that M is also the image of a holomorphic map from any bounded domain in \({\mathbb{C}}^ n\) with \(C^ 2\) boundary. The result is proved by finding an explicit and elementary map from \(B_ n\) to \(\Delta_ n\) which is locally surjective at a prescribed boundary point. The map is neither regular nor finitely fibered, however.