Frontiers of Mathematics in China >

2006 , Vol. 1 >Issue 1: 120 - 129

DOI: https://doi.org/10.1007/s11464-005-0005-3

Complete Quasiconvex Mappings in Polydisc

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  • 1.Department of Mathematics, University of Science and Technology of China, Hefei 230026, China; 2.Department of Mathematics, Shenzhen University, Shenzhen 518060, China;

Published date: 05 Mar 2006

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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.

Cite this article

LIU Tai-shun, ZHANG Wen-jun . Complete Quasiconvex Mappings in Polydisc[J]. Frontiers of Mathematics in China, 2006 , 1(1) : 120 -129 . DOI: 10.1007/s11464-005-0005-3

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