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单叶调和映射
引用本文:张玉林.单叶调和映射[J].数学进展,1993,22(5):402-410.
作者姓名:张玉林
作者单位:西北大学数学系 西安,710069,陕西
摘    要:由于在极小曲面理论中的作用,对调和映射的研究已有较长时间。1984年以来,经典解析单叶映射的理论被推广至调和单叶映射,并获得许多结论。这些工作引起人们对它的浓厚兴趣。该文介绍这一课题某些重要成果的概貌,并指出一些尚未解决的问题。它共分六个部分:映射定理;单叶调和函数的数值估计;特殊映射;变分方法;境界性质和在极小曲面中的应用。

关 键 词:单叶调和映射  映射定理  极小曲面

Univalent Harmonic Mappings
Zhang Yulin.Univalent Harmonic Mappings[J].Advances in Mathematics,1993,22(5):402-410.
Authors:Zhang Yulin
Abstract:Harmonic mappings have long been studied because of the role these mappings play in the theory of minimal surfaces. Since 1984 the classical theory of analytic univalent functions has been generalized, at least in part, to harmonic univalent functions and a lot of results have been gotten. In this paper, a survey of some important results and some open problems are given. It contains six parts: mapping theorems, numerical estimations of univalent harmonic functions, special mappings, variational method, boundary behavior and applications to minimal surfaces.
Keywords:univalent harmonic mappings  mapping theorem  numerical es-timations  variational method  boundary behavior  minimal surfaces
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