研究单位圆盘到水平条形无界区域在原点满足一定规范条件的单叶保向调和映照的解析特征.推导出该类单叶调和映照的解析表示法.得到单位圆盘到水平条形无界区域在原点满足一定规范条件的单叶保向调和映照f（z）成为调和拟共形映照的充分必要条件，对该类调和拟共形映照的系数作出精确估计. 作为应用，证明了该类调和拟共形映照的像在欧氏度量下的长度和面积与原像在非欧度量下的偏差定理.本文的结果改进和推广了由Hengartner和Schober所得的相应结论.
Abstract
We study the analytic characteristic property for sense preserving univalent harmonic mappings on the unit disk onto an infinite horizontal strip domain with a normalization at the origin. By deriving an analytic representing formula for these univalent harmonic mappings, we obtain one necessary and sufficient condition for sense preserving univalent harmonic mappings on the unit disk onto an infinite horizontal strip domain with a normalization at the origin to be harmonic quasiconformal mappings, we also obtain sharp coefficient estimates for these harmonic quasiconformal mappings. As an application, distortion theorems on length and area for image in Euclidean metric between the one for preimage in noneuclidean metric are also obtained. Our results improve and generalize the one made by Hengartner and Schober.
关键词
单叶调和映照 /
调和拟共形映照 /
水平条形无界区域 /
系数估计 /
非欧度量
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Key words
univalent harmonic mapping /
harmonic quasiconformal mapping /
infinitehorizontal strip domain /
coefficient estimate /
noneuclidean metric
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参考文献
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脚注
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基金
国家青年自然科学基金资助项目（11101165）；福建省自然科学基金资助项目（2011J01011）
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