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.


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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