A proof of a weak version of the Bieberbach conjecture in several complex variables  

作　　者：LIU XiaoSong LIU TaiShun XU QingHua 

机构地区：[1]School of Mathematics and Computation Science, Lingnan Normal University [2]Department of Mathematics, Huzhou Teachers College [3]College of Mathematics and Information Science, Jiangxi Normal University

出　　处：《Science China Mathematics》2015年第12期2531-2540,共10页中国科学：数学（英文版）

基　　金：supported by Key Program of National Natural Science Foundation of China(Grant No.11031008);National Natural Science Foundation of China(Grant No.11061015)

摘　　要：In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Our results show that a weak version of the Bieberbach conjecture in several complex variables is proved, and the obtained conclusions reduce to the classical results in one complex variable.In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Our results show that a weak version of the Bieberbach conjecture in several complex variables is proved, and the obtained conclusions reduce to the classical results in one complex variable.

关 键 词：Bieberbach conjecture homogeneous expansion k-fold symmetric mapping a zero of order k ＋ 1 starlike mapping 

分 类 号：O177.2[理学—数学] O174.52[理学—基础数学]