| 黄心中.平面拟共形映照的偏差函数估计[J].数学年刊A辑,2014,35(4):413~422 |
| 平面拟共形映照的偏差函数估计 |
| Estimates of Distortion Functions for Plane Quasiconformal Mappings |
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| DOI： |
| 中文关键词: 拟共形映照, 偏差函数, 模, Grotzsch 环 |
| 英文关键词:Quasiconformal mappings, Distortion functions, Modulus,
Gr\"otzsch ring |
| 基金项目:福建省自然科学基金(No.2011J01011) |
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| 中文摘要: |
| 研究平面拟共形映照的偏差函数 $\mu(r)$, $ \lambda(K)$ 和
$ \eta_K(t)$. 利用环形区域模函数的共形不变性, 证明$\mu(r)$ 满足一个新的不等式. 作为应用, 不必利用椭圆函数的性质, 得到了估计 Gr\"otzsch, Teichm\"uller 和 Mori 这3种典型极值环形区域模函数的更精确的不等式,
并得到了$\lambda(K)$ 和 $\eta_K(t) $ 的更精确的上下界估计不等式. 改进了由 Anderson, Vamanamurthy, Qiu 和 Vuorinen 所得的相应结果. |
| 英文摘要: |
| The author studies distortion functions $\mu(r)$, $ \lambda(K)$ and
$ \eta_K(t)$ of the plane quasiconformal mappings. By the conformal
invariant of the module of a ring domain, a new inequality for
$\mu(r)$ is proved. As its application, without using the elliptic
function, three sharper inequalities concerning the modular
functions for Gr\"otzsch, Teichm\"uller and Mori extremal ring
domains are proved. Better upper and lower bound estimates for
$\lambda(K)$ and $\eta_K(t) $ are also obtained. These results improve
the one made by Anderson, Vamanamurthy, Qiu and Vuorinen. |
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