Abstract:

Let $om$ 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 $om$, 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.

Key words: Spiral-like mappings, parametric representation, growth theorem