上半平面到其自身的调和同胚  

Harmonic homeomorphism of the upper half-plane onto itself

作　　者：扈振永 王麒翰 龙波涌[1] HU Zhen-yong;WANG Qi-han;LONG Bo-yong(School of Mathematical Sciences, Anhui University, Hefei 230601, China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《高校应用数学学报（A辑）》2019年第1期59-64,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11501001);安徽省高校自然科学研究重点项目(KJ2017A029);安徽大学科研项目(Y01002428)

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.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.

关 键 词：调和同胚 拟共形映照 延拓 

分 类 号：O174.51[理学—数学]