Minimal Surfaces in Euclidean 3-Space and Their Mean Curvature 1 Cousins in Hyperbolic 3-Space

Shoich Fujimori

doi:10.1590/S0001-37652003000300002

Minimal Surfaces in Euclidean 3-Space and Their Mean Curvature 1 Cousins in Hyperbolic 3-Space

Shoich Fujimori

研究成果 › 査読

2 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	271-278
ページ数	8
ジャーナル	Anais da Academia Brasileira de Ciencias
巻	75
号	3
DOI	https://doi.org/10.1590/S0001-37652003000300002
出版ステータス	Published - 9月 2003
外部発表	はい

ASJC Scopus subject areas

一般

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10.1590/S0001-37652003000300002

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引用スタイル

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AB - 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.

KW - CMC 1 cousins

KW - Hyperbolic space

KW - Minimal surfaces

UR - https://www.scopus.com/pages/publications/0141456320

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U2 - 10.1590/S0001-37652003000300002

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Minimal Surfaces in Euclidean 3-Space and Their Mean Curvature 1 Cousins in Hyperbolic 3-Space

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