Biholomorphic convex mappings of the ball in \(\mathbb{C}^ n\). (English) Zbl 0788.32017
Biholomorphic convex mappings from the unit ball in \(\mathbb{C}^ n\) into \(\mathbb{C}^ n\) are studied in this paper. A Schwartz type lemma for the class of mappings and a necessary and sufficient condition under which a holomorphic mapping is biholomorphic and convex are established. The results are used to describe some characteristics of the image of the class of mappings.
Reviewer: S.Gong (Beijing)
MSC:
32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
32A22 | Nevanlinna theory; growth estimates; other inequalities of several complex variables |