Starlike mappings on bounded balanced domains with \(C^1\)-plurisubharmonic defining functions (Q1587555)

Let \(D\) be a bounded balanced domain in \(\mathbb{C}^n\) with \(C^1\) plurisubharmonic defining function. The author gives a necessary and sufficient condition for a locally biholomorphic mapping from \(D\) into \(\mathbb{C}^n\) to be starlike. A growth theorem for normalized starlike mappings is also derived. Finally, the author gives a quasiconformal extension of strongly starlike mappings defined on \(D\).