Higher-genus mean curvature-one catenoids in hyperbolic and de sitter 3-spaces

Shoichi Fujimori; Wayne Rossman

doi:10.2206/kyushujm.64.169

Higher-genus mean curvature-one catenoids in hyperbolic and de sitter 3-spaces

Shoichi Fujimori, Wayne Rossman

Graduate School of Natural Science and Technology

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

2 Citations (Scopus)

Abstract

We show the existence of constant mean curvature-one surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter 3-space, but with a different non-embedded end behavior-c.

Original language	English
Pages (from-to)	169-180
Number of pages	12
Journal	Kyushu Journal of Mathematics
Volume	64
Issue number	2
DOIs	https://doi.org/10.2206/kyushujm.64.169
Publication status	Published - 2010

Keywords

Constant mean curvature-one surface
De sitter 3-space
Higher-genus surface
Hyperbolic 3-space

ASJC Scopus subject areas

Mathematics(all)

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10.2206/kyushujm.64.169

Cite this

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abstract = "We show the existence of constant mean curvature-one surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter 3-space, but with a different non-embedded end behavior-c.",

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AB - We show the existence of constant mean curvature-one surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter 3-space, but with a different non-embedded end behavior-c.

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KW - De sitter 3-space

KW - Higher-genus surface

KW - Hyperbolic 3-space

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Higher-genus mean curvature-one catenoids in hyperbolic and de sitter 3-spaces

Abstract

Keywords

ASJC Scopus subject areas

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