Covering properties of most entire functions on Stein manifolds (Q816264)

The authors show that on a Stein manifold, a piecewise holomorphic function can be simultaneously approximated and interpolated together with finitely many derivatives by a global holomorphic function under certain conditions, thus generalizing a 1-dimensional result. As a consequence they show that for each point \(p\) of a Stein manifold \(X\) there exists an open neighborhood \(U\) of \(p\), biholomorphic to a polydisc, such that each compact subset of \(U\) which is \(U\)-convex is also \(X\)-convex. They also show that most equidimensional holomorphic mappings into complex Euclidian space contain arbitrarily large ``schlicht'' balls in their images and that most global holomorphic functions have a universality property with respect to the approximation of local functions.