Minimal surfaces in euclidean 3-space and their mean curvature 1 cousins in hyperbolic 3-space

被引：1
|
作者：
Fujimori, S [1 ]
机构：
[1] Kobe Univ, Dept Math, Kobe, Hyogo 6578501, Japan
来源：
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS | 2003年 / 75卷 / 03期
关键词：
minimal surfaces; CMC; 1; cousins; hyperbolic space;
D O I：
10.1590/S0001-37652003000300002
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We show that the Hopf differentials of a pair of isometric cousin surfaces, a minimal surface in euclidean 3-space and a constant mean curvature (CMC) one surface in the 3-dimensional hyperbolic space, with properly embedded annular ends, extend holomorphically to each end. Using this result, we derive conditions for when the pair must be a plane and a horosphere.
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页码：271 / 278
页数：8
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