Complete Quasiconvex Mappings in Polydisc |
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| Authors: | Tai-shun Liu Wen-jun Zhang |
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| Institution: | (1) Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China;(2) Department of Mathematics, Shenzhen University, Shenzhen, 518060, China |
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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 ℂ
n
. 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.
Translated from Chinese Annals of Mathematics (Series A) |
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| Keywords: | bounded convex Reinhardt domain complete quasiconvex mapping quasiconvex mapping convex mapping decomposition theorem |
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