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

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.

Article information

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

Dates
First available in Project Euclid: 3 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1317647397

Digital Object Identifier
doi:10.3792/pjaa.87.144

Mathematical Reviews number (MathSciNet)
MR2843096

Zentralblatt MATH identifier
1242.53070

Citation

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. https://projecteuclid.org/euclid.pja/1317647397

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