Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps

摘要

We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. We first show that for any bounded convex domain Omega (sic) C-n and any connected complex manifold Y, the space O(Omega, Y) contains a dense holomorphic disc. Our second result states that Y is an Oka manifold if and only if for any Stein space X there exists a dense entire curve in every path component of O(X, Y).