Discs in the ball containing given discrete sets (Q1118074)

In this very technical paper, needing seven lemmas the author proves the following theorem. Theorem. Every closed discrete subset of the unit ball of \({\mathbb{C}}^ n\) is contained in a variety of the form f(\(\Delta)\), where \(\Delta\) denotes the open unit disc of \({\mathbb{C}}\) and f denotes a proper holomorphic immersion. The map can be chosen to extend continuously to the closure of the unit disc minus one.