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arXiv · 0804.4198

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

Wayne Rossman
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Abstract

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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Wayne Rossman. 2008-04-26. Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space. https://arxiv.org/abs/0804.4198

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