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; Kotaro Yamada

doi:10.3792/pjaa.87.144

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, Kotaro Yamada

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

CMC-1 trinoids (i.e. constant mean curvature one immersed surfaces of genus zero with three regular embedded ends) in hyperbolic 3-space H³ 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 H³ that includes the reducible case.

Original language	English
Pages (from-to)	144-149
Number of pages	6
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	87
Issue number	8
DOIs	https://doi.org/10.3792/pjaa.87.144
Publication status	Published - 2011

Keywords

Conical singularities
Constant mean curvature
Spherical metrics
Trinoids

ASJC Scopus subject areas

Mathematics(all)

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10.3792/pjaa.87.144

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T1 - CMC-1 trinoids in hyperbolic 3-space and metrics of constant curvature one with conical singularities on the 2-sphere

AU - Fujimori, Shoichi

AU - Kawakami, Yu

AU - Kokubu, Masatoshi

AU - Rossman, Wayne

AU - Umehara, Masaaki

AU - Yamada, Kotaro

PY - 2011

Y1 - 2011

N2 - CMC-1 trinoids (i.e. constant mean curvature one immersed surfaces of genus zero with three regular embedded ends) in hyperbolic 3-space H3 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 H3 that includes the reducible case.

AB - CMC-1 trinoids (i.e. constant mean curvature one immersed surfaces of genus zero with three regular embedded ends) in hyperbolic 3-space H3 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 H3 that includes the reducible case.

KW - Conical singularities

KW - Constant mean curvature

KW - Spherical metrics

KW - Trinoids

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

Abstract

Keywords

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