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

Approximation of holomorphic maps with a lower bound on the rank