Complete Quasiconvex Mappings in Polydisc

Abstract

In this paper, a class of biholomorphic mappings called complete quasiconvex mappings is introduced and studied in bounded convex Reinhardt domains of Cⁿ. Through a detailed analysis of the analytic characterization for this class of mappings, it is shown that this class of mappings contains the convex mappings and is also a subset of the class of starlike mappings. In the special case of the polydisc, a decomposition theorem is established for the complete quasiconvex mappings, which in turn is used to derive an improved sufficient condition for the convex mappings.