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。
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.
出处
《数学进展》
CSCD
北大核心
1993年第5期402-410,共9页
Advances in Mathematics（China）
基金
国家自然科学基金
关键词
单叶调和映射
映射定理
极小曲面
univalent harmonic mappings
mapping theorem
numerical es-timations
variational method
boundary behavior
minimal surfaces
