Runge tubes in Stein manifolds with the density property

In this paper we give a simple proof of the existence and plenitude of Runge tubes in C-n (n > 1) and, more generally, in Stein manifolds with the density property. We show in particular that for any algebraic submanifold X of codimension at least two in a complex Euclidean space C-n, the normal bundle of X admits a holomorphic embedding onto a Runge domain in C-n which agrees with the inclusion map X hooked right arrow C-n on the zero section.