Illinois Journal of Mathematics

New constant mean curvature surfaces in the hyperbolic space

K. Tenenblat and Q. Wang

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Abstract

Applying Ribaucour transformations, we construct two new 3-parameter families of complete surfaces, immersed in $H^3$, with constant mean curvature 1 and infinitely many embedded horosphere type ends. Each surface of the first family is locally associated to an Enneper cousin. It has one irregular end and infinitely many regular ends asymptotic to horospheres. The surfaces of the second family are locally associated to a catenoid cousin. Each surface of this family has infinitely many embedded horosphere type ends and one regular end with infinite total curvature.

Article information

Source
Illinois J. Math., Volume 53, Number 1 (2009), 135-161.

Dates
First available in Project Euclid: 22 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1264170843

Digital Object Identifier
doi:10.1215/ijm/1264170843

Mathematical Reviews number (MathSciNet)
MR2584939

Zentralblatt MATH identifier
1194.53051

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Citation

Tenenblat, K.; Wang, Q. New constant mean curvature surfaces in the hyperbolic space. Illinois J. Math. 53 (2009), no. 1, 135--161. doi:10.1215/ijm/1264170843. https://projecteuclid.org/euclid.ijm/1264170843


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