基于特殊幂级数的双曲完备极小曲面研究

Research on Hyperbolic Complete Minimal Surfaces Based on Special Power Series

摘要: 在双曲完备极小曲面及Hadamard缺项幂级数的研究背景下，以Brito构造ℝ3中位于两个平行平面间完备极小曲面族的方法为基础，利用Holder不等式、Cauchy-Schwarz不等式对拆分成多项的|Ck|进行放缩，比较不同不等式的放缩效果，使得|Ck|尽可能小，从而使得h(z)适用条件扩大，且找到在某个范围条件下的双曲完备极小曲面族，丰富相关实例。

Abstract: In the context of the study on hyperbolic complete minimal surfaces and power series with Hadamard gaps, based on the method of Brito’s construction of a family of complete minimal surfaces between two parallel planes inℝ3, we use Holder inequality and Cauchy-Schwarz inequality to scale the|Ck|which is splited into multiple terms, and compare the scale effects of the different inequalities to make the|Ck|as small as possible, to make the applicable conditions ofh(z)wider. And families of hyperbolic complete minimal surfaces are found under a range of conditions, enriching the relevant examples.