具有Hadamard缺项幂级数的双曲完备极小曲面

Hyperbolic Complete Minimal Surfaces with Power Series of Hadamard Gaps

摘要: 对具有Hadamard间隙的某缺项幂级数增加或减弱适当的条件，利用Brito构造R³中位于两个平行平面间完备极小曲面族的方法，将和式拆分为三项估计项，利用Cauchy-Schwarz不等式对估计项进行放缩，修正并进一步精确范围以继续构造极小曲面，给出实例。在此基础上利用Weierstrass表示对寻找R³中一个完备极小曲面的Gauss映射。

Abstract: For a special power series with Hadamard gaps increasing or decreasing appropriate conditions, using Brito’s method of constructing a complete minimal surface family between two parallel planes in R³, the sum was split into three estimated terms, and Cauchy-Schwarz inequality was used to scale the estimated terms. The range was modified and further refined to continue the construction of minimal surfaces. Examples were given. On this basis, Weierstrass representation pair was used to find a Gauss map of a complete minimal surface in R³.