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Spring 2009 New constant mean curvature surfaces in the hyperbolic space
K. Tenenblat, Q. Wang
Illinois J. Math. 53(1): 135-161 (Spring 2009). DOI: 10.1215/ijm/1264170843


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.


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K. Tenenblat. Q. Wang. "New constant mean curvature surfaces in the hyperbolic space." Illinois J. Math. 53 (1) 135 - 161, Spring 2009.


Published: Spring 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1194.53051
MathSciNet: MR2584939
Digital Object Identifier: 10.1215/ijm/1264170843

Primary: 53C20

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign


Vol.53 • No. 1 • Spring 2009
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