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

作　　者：邵煜 

机构地区：[1]上海理工大学理学院,上海

出　　处：《理论数学》2024年第5期315-323,共9页Pure Mathematics

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。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.

关 键 词：完备极小曲面 Hadamard缺项幂级数 发散曲线 HOLDER不等式 

分 类 号：O17[理学—数学]