| 上半平面到其自身的调和同胚 |
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| 引用本文： | 扈振永,王麒翰,龙波涌.上半平面到其自身的调和同胚[J].高校应用数学学报(A辑),2019,34(1):59-64. |
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| 作者姓名： | 扈振永 王麒翰 龙波涌 |
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| 作者单位： | 安徽大学 数学科学学院,安徽合肥,230601;安徽大学 数学科学学院,安徽合肥,230601;安徽大学 数学科学学院,安徽合肥,230601 |
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| 基金项目： | 国家自然科学基金;安徽省高等学校自然科学研究重点项目;大学科研项目 |
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| 摘 要： | 得到了实轴R上的保向同胚φ(x)在Beurling-Ahlfors延拓下是调和拟共形的充要条件.利用poisson积分具体给出了一个φ(x)延拓成上半平面到其自身的调和同胚.并且给出了这个调和同胚为拟共形的一个充分条件,得到了它的伸张估计.所得结果推广了Michalski的相关结果.
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| 关 键 词： | 调和同胚 拟共形映照 延拓 |
Harmonic homeomorphism of the upper half-plane onto itself |
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| HU Zhen-yong,WANG Qi-han,LONG Bo-yong.Harmonic homeomorphism of the upper half-plane onto itself[J].Applied Mathematics A Journal of Chinese Universities,2019,34(1):59-64. |
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| Authors: | HU Zhen-yong WANG Qi-han LONG Bo-yong |
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| Institution: | (School of Mathematical Sciences, Anhui University, Hefei 230601, China) |
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| Abstract: | In this paper, the necessary and sufficient conditions for the extension of Beurling- Ahlfors to be a harmonic quasiconformal mapping of the upper half-plane onto itself are obtained. Specifically, a kind of harmonic homeomorphism of the upper half-plane by applying poisson integral is considered. Furthermore, a sufficient condition for this harmonic homeomorphism to be quasiconformal is presented, and its dilatation is estimated. Some results of Michalski are generalized. |
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| Keywords: | harmonic homeomorphism quasiconformal mapping extension |
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