Liu, Xiaosong; Liu, Taishun On the sharp growth covering theorems for normalized biholomorphic mappings in \(\mathbb{C}^n\). (English) Zbl 1150.30005 Acta Math. Sci., Ser. B, Engl. Ed. 27, No. 4, 803-812 (2007). Summary: In this article, a normalized biholomorphic mapping \(f\) defined on bounded starlike circular domain in \(\mathbb{C}^n\) is considered, where \(z=0\) is a zero of order \(k+1\) of \(f (z)-z\). The sharp growth, covering theorems for almost starlike mappings of order \(\alpha\) and starlike mappings of order \(\alpha\) are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in \(\mathbb{C}^n\) is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings. Cited in 3 Documents MSC: 30C25 Covering theorems in conformal mapping theory 32A30 Other generalizations of function theory of one complex variable 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:zero of order \(k+1\); normalized biholomorphic mappings; almost starlike mappings; starlike mappings; growth; covering theorems PDFBibTeX XMLCite \textit{X. Liu} and \textit{T. Liu}, Acta Math. Sci., Ser. B, Engl. Ed. 27, No. 4, 803--812 (2007; Zbl 1150.30005) Full Text: DOI