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

被引：0
|
作者：
LIU XiaoSong [1 ]
LIU TaiShun [2 ]
XU QingHua [3 ]
机构：
[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
来源：
Science China(Mathematics) | 2015年 / 58卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Bieberbach conjecture; homogeneous expansion; k-fold symmetric mapping; a zero of order k + 1; starlike mapping;
D O I：
暂无
中图分类号：
O177.2 [巴拿赫空间及其线性算子理论]; O174.52 [整数函数论、亚纯函数论（半纯函数论）];
学科分类号：
070104 ;
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.
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页码：2531 / 2540
页数：10
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