Meromorphic functions and the Gauss map of complete minimal surfaces
Meromorphic functions and the Gauss map of complete minimal surfaces
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亚纯函数和完整极小曲面的高斯图
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Yuhua Li
中科院分区：
文献类型：
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作者：
Min Su;Yuhua Li
本文给出了复平面上亚纯函数是某个完备极小曲面的Gauss映射的一个条件。事实上，我们证明了：如果g1（z）和g2（z）（不相等0）是没有公共零点的整函数，至少它们的一个Taylor展开式在原点有2−阶费耶尔间隙，那么亚纯函数g1（z）/g2（z）可以看作是某些完备极小曲面的Gauss映射.
In this paper, we obtain a condition which guarantees the meromorphic function on the complex plane is the Gauss map of some complete minimal surface. In fact, we prove that if g1(z) and g2(z)(not indentical 0) are entire functions which have no common zeros at least one of their Taylor expansions at the origin has 2−order Fejer gaps, then the meromorphic function g1(z)/g2(z) can be viewed as the Gauss map of some complete minimal surfaces.