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

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	271-278
Number of pages	8
Journal	Anais da Academia Brasileira de Ciencias
Volume	75
Issue number	3
DOIs	https://doi.org/10.1590/S0001-37652003000300002
Publication status	Published - Sept 2003
Externally published	Yes

Keywords

CMC 1 cousins
Hyperbolic space
Minimal surfaces

ASJC Scopus subject areas

General

Access to Document

10.1590/S0001-37652003000300002

Cite this

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abstract = "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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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

UR - https://www.scopus.com/pages/publications/0141456320#tab=citedBy

U2 - 10.1590/S0001-37652003000300002

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M3 - Article

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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