Annals of Global Analysis and Geometry

, Volume 40, Issue 2, pp 167–176

New complete embedded minimal surfaces in \({{\mathbb {H} ^2\times \mathbb {R}}}\)

Original Paper

DOI: 10.1007/s10455-011-9251-7

Cite this article as:
Pyo, J. Ann Glob Anal Geom (2011) 40: 167. doi:10.1007/s10455-011-9251-7


We construct three kinds of complete embedded minimal surfaces in \({\mathbb {H}^2\times \mathbb {R}}\) . The first is a simply connected, singly periodic, infinite total curvature surface. The second is an annular finite total curvature surface. These two are conjugate surfaces just as the helicoid and the catenoid are in \({\mathbb {R}^3}\) . The third one is a finite total curvature surface which is conformal to \({\mathbb {S}^2\setminus\{p_1,\ldots,p_k\}, k\geq3.}\)


Complete minimal surfaceFinite total curvatureProduct space

Mathematics Subject Classification (2000)

Primary 53C42Secondary 53A3553C40

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Korea Institute for Advanced StudySeoulKorea