Tohoku Mathematical Journal

Surfaces of constant mean curvature one in the hyperbolic three-space with irregular ends

Zuhuan Yu

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Abstract

We investigate surfaces of constant mean curvature one in the hyperbolic three-space with irregular ends, and prove that their irregular ends must self-intersect, which answers affirmatively a conjecture of Umehara and Yamada. Moreover we also obtain an explicit representation of a constant mean curvature one surface and a new minimal surface in the Euclidean three-space.

Article information

Source
Tohoku Math. J. (2), Volume 53, Number 2 (2001), 305-318.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178207483

Digital Object Identifier
doi:10.2748/tmj/1178207483

Mathematical Reviews number (MathSciNet)
MR1829983

Zentralblatt MATH identifier
1027.53011

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53A35: Non-Euclidean differential geometry

Citation

Yu, Zuhuan. Surfaces of constant mean curvature one in the hyperbolic three-space with irregular ends. Tohoku Math. J. (2) 53 (2001), no. 2, 305--318. doi:10.2748/tmj/1178207483. https://projecteuclid.org/euclid.tmj/1178207483


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References

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