Gong, Sheng; Wang, Shikun; Yu, Qihuang Biholomorphic convex mappings of the ball in \(\mathbb{C}^ n\). (English) Zbl 0788.32017 Pac. J. Math. 161, No. 2, 287-306 (1993). 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) Cited in 2 ReviewsCited in 23 Documents MSC: 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables Keywords:biholomorphic convex mappings; second fundamental form; principal curvature; Schwartz type lemma PDFBibTeX XMLCite \textit{S. Gong} et al., Pac. J. Math. 161, No. 2, 287--306 (1993; Zbl 0788.32017) Full Text: DOI