### Abstract

We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is an 'elliptic end' (respectively a 'hyperbolic end') if the monodromy matrix at the end is diagonalizable with eigenvalues in the unit circle (respectively in the reals). Although the existence of the surfaces is numerical, the types of ends are mathematically determined.

Original language | English |
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Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Kyushu Journal of Mathematics |

Volume | 61 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 7 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- De Sitter 3-space
- Genus 1 surface
- Spacelike constant mean curvature 1 surface

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Spacelike mean curvature 1 surfaces of genus 1 with two ends in de Sitter 3-space.** / Fujimori, Shoichi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Spacelike mean curvature 1 surfaces of genus 1 with two ends in de Sitter 3-space

AU - Fujimori, Shoichi

PY - 2007/6/7

Y1 - 2007/6/7

N2 - We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is an 'elliptic end' (respectively a 'hyperbolic end') if the monodromy matrix at the end is diagonalizable with eigenvalues in the unit circle (respectively in the reals). Although the existence of the surfaces is numerical, the types of ends are mathematically determined.

AB - We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is an 'elliptic end' (respectively a 'hyperbolic end') if the monodromy matrix at the end is diagonalizable with eigenvalues in the unit circle (respectively in the reals). Although the existence of the surfaces is numerical, the types of ends are mathematically determined.

KW - De Sitter 3-space

KW - Genus 1 surface

KW - Spacelike constant mean curvature 1 surface

UR - http://www.scopus.com/inward/record.url?scp=34548243167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548243167&partnerID=8YFLogxK

U2 - 10.2206/kyushujm.61.1

DO - 10.2206/kyushujm.61.1

M3 - Article

VL - 61

SP - 1

EP - 20

JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

SN - 1340-6116

IS - 1

ER -