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**CMC-1 trinoids in hyperbolic 3-space and metrics of constant curvature one with conical singularities on the 2-sphere.**
*(English)*
Zbl 1242.53070

Authors’ abstract: CMC-1 trinoids (i.e. constant mean curvature one immersed surfaces of genus zero with three regular embedded ends) in hyperbolic 3-space \(H^{3}\) are irreducible generically, and the irreducible ones have been classified. However, the reducible case has not yet been fully treated, so here we give an explicit description of CMC-1 trinoids in \(H^{3}\) that includes the reducible case.

Reviewer: Erich Hoy (Friedberg)

### MSC:

53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |

53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |

53A35 | Non-Euclidean differential geometry |

33C05 | Classical hypergeometric functions, \({}_2F_1\) |

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\textit{S. Fujimori} et al., Proc. Japan Acad., Ser. A 87, No. 8, 144--149 (2011; Zbl 1242.53070)

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