THE PARAMETRIC REPRESENTATION FOR SPIRAL-LIKE MAPPINGS OF TYPE α ON BOUNDED BALANCED PSEUDOCONVEX DOMAINS*

Let Ω be a bounded balanced pseudoconvex domain in ℂn that admits a plurisubhamonic defining function of class C2. The authors prove that if f is a spiral-like mapping of type α on Ω, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type α are obtained. As a direct application, the growth theorem for spiral-like mappings of type α is set up.