Entire curves avoiding given sets in C^n

Abstract

Let $F\subset {\mathbb{C}}^n$ be a proper closed subset of ${\mathbb{C}}^n$ and $A\subset {\mathbb{C}}^n\setminus F$ at most countable ($n\ge 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\varphi :\mathbb{C}\to {\mathbb{C}}^n$ with $A\subset \varphi (\mathbb{C})\subset {\mathbb{C}}^n\setminus F$.

arXiv comment10 pages