Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space

Details Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space

2008-04-26

arxiv.org/abs/0804.4198v1

J. Geom. Anal. 11(4) (2001), 669-692

Mathematics

Differential Geometry

Scientific paper

We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean curvature 1 surfaces in hyperbolic 3-space, and we give an overview of recent results on these surfaces. We include computer graphics of a number of examples.

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