Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range C-n

In this paper we study the class of "shearing" holomorphic maps of the unit ball of the form (z ,w) bar right arrow (z + g(w), w). Besides general properties, we use such maps to construct an example of a normalized univalent map of the ball onto a Runge domain in C-n which however cannot be embedded into a Loewner chain whose range is C-n.