Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space
Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space
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德西特3空间中常平均曲率一几何悬链线的解析推广
DOI：
10.1016/j.difgeo.2022.101924
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发表时间：
2022
影响因子：
0.5
通讯作者：
Kotaro Yamada and Seong-Deog Yang
中科院分区：
文献类型：
--
作者：
Shoichi Fujimori;Yu Kawakami;Masatoshi Kokubu; Wayne Rossman;Masaaki Umehara;Kotaro Yamada and Seong-Deog Yang
证明了一个真实的解析映射的象的“解析完备性”的简单概念意味着该映射不允许解析扩张。我们还通过定义连续映射的弧恰当性给出了分析完备性概念的一个有用的判据，弧恰当性可以被认为是恰当性的一个非常弱的版本。作为应用，我们在de Sitter三维空间中判定了一类常平均曲率曲面（所谓的“G-悬链面”）或其解析扩张的解析完备性。
We show that a certain simply-stated notion of “analytic completeness” of the image of a real analytic map implies the map admits no analytic extension. We also give a useful criterion for that notion of analytic completeness by defining arc-properness of continuous maps, which can be considered as a very weak version of properness. As an application, we judge the analytic completeness of a certain class of constant mean curvature surfaces (the so-called “G-catenoids”) or their analytic extensions in the de Sitter 3-space.