### Abstract

The first author studied spacelike constant mean curvature one (CMC-1) surfaces in the de Sitter 3-space S^{3}
_{1} when the surfaces have no singularities except within some compact subsets and are of finite total curvature on the complement of this compact subset. However, there are many CMC-1 surfaces whose singular sets are not compact. In fact, such examples have already appeared in the construction of trinoids given by Lee and the last author via hypergeometric functions. In this paper, we improve the Osserman-type inequality given by the first author. Moreover, we shall develop a fundamental framework that allows the singular set to be non-compact, and then will use it to investigate the global behavior of CMC-1 surfaces.

Original language | English |
---|---|

Pages (from-to) | 383-427 |

Number of pages | 45 |

Journal | Communications in Analysis and Geometry |

Volume | 17 |

Issue number | 3 |

Publication status | Published - Jul 2009 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistics and Probability
- Geometry and Topology
- Analysis
- Statistics, Probability and Uncertainty

### Cite this

*Communications in Analysis and Geometry*,

*17*(3), 383-427.

**Spacelike mean curvature one surfaces in de Sitter 3-space.** / Fujimori, Shoichi; Rossman, W.; Umehara, M.; Yamada, K.; Yang, S. D.

Research output: Contribution to journal › Article

*Communications in Analysis and Geometry*, vol. 17, no. 3, pp. 383-427.

}

TY - JOUR

T1 - Spacelike mean curvature one surfaces in de Sitter 3-space

AU - Fujimori, Shoichi

AU - Rossman, W.

AU - Umehara, M.

AU - Yamada, K.

AU - Yang, S. D.

PY - 2009/7

Y1 - 2009/7

N2 - The first author studied spacelike constant mean curvature one (CMC-1) surfaces in the de Sitter 3-space S3 1 when the surfaces have no singularities except within some compact subsets and are of finite total curvature on the complement of this compact subset. However, there are many CMC-1 surfaces whose singular sets are not compact. In fact, such examples have already appeared in the construction of trinoids given by Lee and the last author via hypergeometric functions. In this paper, we improve the Osserman-type inequality given by the first author. Moreover, we shall develop a fundamental framework that allows the singular set to be non-compact, and then will use it to investigate the global behavior of CMC-1 surfaces.

AB - The first author studied spacelike constant mean curvature one (CMC-1) surfaces in the de Sitter 3-space S3 1 when the surfaces have no singularities except within some compact subsets and are of finite total curvature on the complement of this compact subset. However, there are many CMC-1 surfaces whose singular sets are not compact. In fact, such examples have already appeared in the construction of trinoids given by Lee and the last author via hypergeometric functions. In this paper, we improve the Osserman-type inequality given by the first author. Moreover, we shall develop a fundamental framework that allows the singular set to be non-compact, and then will use it to investigate the global behavior of CMC-1 surfaces.

UR - http://www.scopus.com/inward/record.url?scp=70350319649&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350319649&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:70350319649

VL - 17

SP - 383

EP - 427

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

SN - 1019-8385

IS - 3

ER -