Proceedings of the Japan Academy, Series A, Mathematical Sciences

CMC-1 trinoids in hyperbolic 3-space and metrics of constant curvature one with conical singularities on the 2-sphere

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

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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.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 8 (2011), 144-149.

First available in Project Euclid: 3 October 2011

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Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53A35: Non-Euclidean differential geometry
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 33C05: Classical hypergeometric functions, $_2F_1$

Constant mean curvature spherical metrics conical singularities trinoids


Fujimori, Shoichi; Kawakami, Yu; Kokubu, Masatoshi; Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro. CMC-1 trinoids in hyperbolic 3-space and metrics of constant curvature one with conical singularities on the 2-sphere. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 8, 144--149. doi:10.3792/pjaa.87.144.

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