| 黄心中,傅冬绵.微分算子作用下平面调和映照的单叶半径和 Bloch 常数估计[J].数学年刊A辑,2013,34(6):653~662 |
| 微分算子作用下平面调和映照的单叶半径和 Bloch 常数估计 |
| Estimates on the Univalent Radius and Bloch Constant for Planar HarmonicMappings Under Differential Operator |
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| DOI： |
| 中文关键词: 调和映照, 稳定性, 微分算子, 单叶半径, Bloch 常数 |
| 英文关键词:Harmonicmapping, Stable, Differential operator, Univalent radius,
Bloch constant |
| 基金项目:国家青年自然科学基金 (No.11101165) 和福建省自然科学基金(No.2011J0101) |
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| 中文摘要: |
| 利用单位圆$D=\{z\mid | z |<1\}$上单叶调和映照的稳定性特征, 研究平面调和映照$f=h+\ov g$在微分算子
$L=z \frac {\partial }{\partial z}-\ov {z}\frac {\partial}{\partial {\ov z}}$作用下调和映照的单叶半径和 Bloch 常数估计, 得到一些精确性结论, 并改进了近期由刘名生和刘志文所得的相应结果. |
| 英文摘要: |
| Using the stable properties of univalent harmonic
mappings in the unit disk $D=\{z\mid | z |<1\}$, the authors estimate
the univalent radius and Bloch constant for planar harmonic mappings under
differential operator $L=z \frac {\partial }{\partial
z}-\ov {z}\frac {\partial}{\partial {\ov z}}$. Several sharp
results are obtained, and some results recently obtained by Mingsheng Liu and
Zhiwen Liu are improved. |
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