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.

Keywords

bounded convex Reinhardt domain / complete quasiconvex mapping / quasiconvex mapping / convex mapping / decomposition theorem / 32A30 / 32H02

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