%0 Journal Article
%T 基于特殊幂级数的双曲完备极小曲面研究<br>Research on Hyperbolic Complete Minimal Surfaces Based on Special Power Series
%A 邵煜
%J Pure Mathematics
%P 315-323
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/pm.2024.145188
%X 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？3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。<br />
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 in？3, 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.
%K 完备极小曲面，Hadamard缺项幂级数，发散曲线，Holder不等式<br>Complete Minimal Surface
%K Power Series with Hadamard Gaps
%K Divergent Curves
%K Holder Inequality
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=87754