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

Fujimori, Shoichi; Kawakami, Yu; Kokubu, Masatoshi; Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro

Proc. Japan Acad., Ser. A 87, No. 8, 144-149 (2011).

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, \({}_2F_1\)

Keywords:

constant mean curvature; spherical metrics; conical singularities; trinoids

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