## Abstract

We prove that a properly embedded annular end of a surface in H^{2} X R with constant mean curvature 0 < H ≤ 1=2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 1=2 contained in H^{2} X Œ0; C1/ and with finite topology is necessarily a graph over a simply connected domain of H^{2}. For the case H D 1=2, the graph is entire.

Original language | English (US) |
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Pages (from-to) | 307-320 |

Number of pages | 14 |

Journal | Revista Matematica Iberoamericana |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - 2023 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Constant mean curvature surface
- halfspace theorem
- slab theorem

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