单位圆盘外单叶调和映射的面积定理  

Area Theorem of Univalent Harmonic Mappings Outside Unit Disk

作　　者：石擎天 林珍连[2] SHI Qingtian;LIN Zhenlian(School of Mathematics and Computation Science,Quanzhou Normal University,Quanzhou 362000,China;School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]泉州师范学院数学与计算机科学学院,福建泉州362000 [2]华侨大学数学科学学院,福建泉州362021

出　　处：《集美大学学报（自然科学版）》2022年第4期365-369,共5页Journal of Jimei University：Natural Science

基　　金：福建省自然科学基金青年创新项目(2020J05157);福建省中青年教师教育科研项目(JAT190508)。

摘　　要：设Σ_(H)是所有单位圆盘外部Δ^(*)上单叶保向的规范化调和映射。利用Green定理得到了Σ_(H)类的面积定理,并运用该面积定理和Cauchy-Green公式,对具有拟共形延拓性的Σ_(H)类函数的系数进行估计。所得结果推广了经典的Σ类相应结果。LetΣ_(H)be the class of all sense preserving univalent and normalization harmonic mappings on the exterior of the unit diskΔ^(*).Using the Green theorem,the area theorem of Σ_(H) was obtained.Then applying this area theorem and Cauchy-Green formula,the coefficients estimation of Σ_(H) with quasiconformal extension to the plane was studied.The results generalize the corresponding results of the classicalΣ.

关 键 词：单叶调和映射 拟共形延拓 面积定理 Green定理 

分 类 号：O174.51[理学—数学]