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Barnard, FitzGerald and Gong [1] and Chuaqui [2] extended this to normalized starlike mappings on the unit ball Bn in Cn. Their proof uses the characterization of the starlikeness due to Suffridge [11]. Chuaqui [2] also obtained a quasiconformal extension of some strongly starlike mapping on Bn. In this paper, we will extend the above results to (strongly) starlike mappings on bounded balanced domains with C1 plurisubharmonic defining functions in Cn. Since we cannot use the characterization of the starlikeness due to Suffridge [11], we first give a necessary and sufficient condition that a locally biholomorphic mapping on such domains is starlike using the idea of Gong, Wang and Yu [4]. To prove that condition, a Schwarz type lemma on balanced pseudoconvex domains [5], [6] is needed.

Starlike mappings on bounded balanced domains with C1-plurisubharmonic defining functions

Starlike mappings on bounded balanced domains with C¹-plurisubharmonic defining functions