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

Anais da Academia Brasileira de Ciências

Shoichi Fujimori¹ 

[1] ,KobeUniversity Department of Mathematics ,Japan

关键词: minimal surfaces;    CMC 1 cousins;    hyperbolic space;    superfícies mínimas;    prismas de CMC 1;    espaços hiperbólicos;   

DOI  :  10.1590/S0001-37652003000300002

来源: SciELO

【 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.

【 授权许可】

CC BY   
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