  Let $K$ be a closed polydisc or ball in $\C^n$, and let $Y$ be a quasi
projective algebraic manifold which is Zariski locally equivalent to $\C^p$, or
a complement of an algebraic subvariety of codimension $\ge 2$ in such
manifold. If $r$ is an integer satisfying $(n-r+1) (p-r+1)\geq 2$ then every
holomorphic map from a neighborhood of $K$ to $Y$ with rank $\ge r$ at every
point of $K$ can be approximated uniformly on $K$ by entire maps $\C^n\to Y$
with rank $\ge r$ at every point of $\C^n$.
