The spherical metric and univalent harmonic mappings
The spherical metric and univalent harmonic mappings
复制标题
球面度量和一价调和映射
DOI：
10.1007/s00605-018-1160-4
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
S. Ponnusamy
中科院分区：
文献类型：
--
作者：
Y. Abu Muhanna;R. Ali;S. Ponnusamy
设 为单位圆盘中的调和一价映射，其中进行解析。本文发现了对 h 的第二个系数的改进估计。事实上，这一估计是自 Clunie 和 Sheil-Small (Ann Acad Sci Fenn Ser A I 9:3-25, 1984) 以及 Sheil-Small (J Lond Math Soc 42:237-248, 1990) 论文发表以来的首次质量改进。当扩张的超范数小于1时，也表明其覆盖面的球形面积受覆盖面的球形面积支配。
Letbe a harmonic univalent map in the unit disk, wherehandgare analytic. This paper finds an improved estimate for the second coefficient ofh. Indeed, this estimate is the first qualitative improvement since the appearance of the papers by Clunie and Sheil-Small (Ann Acad Sci Fenn Ser A I 9:3–25, 1984), and by Sheil-Small (J Lond Math Soc 42:237–248, 1990). When the sup-norm of the dilatation is less than 1, it is also shown that the spherical area of the covering surface ofhis dominated by the spherical area of the covering surface off.