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| 摘要: |
| 本文研究了平面调和映射的可积拟共形延拓问题.利用经典的共形映射的拟共形延拓方法和调和映射的性质，获得了一些条件使得调和映射可以拟共形延拓至整个平面且其复伸缩商关于双曲度量是p次可积的，推广了解析单叶函数的相关结果. |
| 关键词: 调和映射 拟共形延拓 Pre-Schwarzaian导数 Schwarzaian导数 |
| DOI： |
| 分类号:O175 |
| 基金项目:国家自然科学基金资助（11701459，11601100）；西华师范大学博士启动基金（17E088）；贵州省科技厅基金资助（[2017]7337，[2017]5726）；四川省教育厅基金（17ZB0431）. |
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| INTEGRABLE QUASICONFORMAL EXTENSION OF HARMONIC MAPPINGS |
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TANG Shu-an,FENG Xiao-gao
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| Abstract: |
| In this paper, we study the integrable quasiconformal extension of harmonic mappings in the plane. By using the classical method of quasiconformal extension of conformal mapping and some properties of harmonic mappings, we obtain some conditions to ensure the harmonic mapping can be quasiconformally extended to the whole complex plane so that its complex dilatation is p integrable with respect to the hyperbolic metric. These results generalize the related results of univalent analytic functions. |
| Key words: harmonic mappings quasiconformal extension Pre-Schwarzian derivative Schwarzian derivative |
