## Abstract

We prove an Alexandrov-type theorem for a quotient space of ℍ^{2}×ℝ. More precisely, we classify the compact embedded surfaces with constant mean curvature in the quotient of ℍ^{2}×R by a subgroup of isometries generated by a horizontal translation along horocycles of ℍ^{2} and a vertical translation. We also construct some examples of periodic minimal surfaces in ℍ^{2}×ℝ and we prove a multivalued Rado theorem for small perturbations of the helicoid in ℍ^{2}×ℝ.

Original language | English (US) |
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Pages (from-to) | 155-172 |

Number of pages | 18 |

Journal | Pacific Journal of Mathematics |

Volume | 268 |

Issue number | 1 |

DOIs | |

State | Published - 2014 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Alexandrov reflection
- Constant mean curvature surface
- Periodic surface

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