Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded
Differential Geometry
2012-05-23 v1
Abstract
We construct a weakly complete flat surface in hyperbolic 3-space having a pair of hyperbolic Gauss maps both of whose images are contained in an arbitrarily given open disc in the ideal boundary of H^3. This construction is accomplished as an application of the minimal surface theory. This looks an interesting phenomenon if one comparing the fact that there are no complete minimal (resp. constant mean curvature one) surfaces in R^3 (resp. H^3) having bounded Gauss maps (resp. bounded hyperbolic Gauss maps).
Cite
@article{arxiv.1205.4779,
title = {Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded},
author = {Francisco Martin and Masaaki Umehara and Kotaro Yamada},
journal= {arXiv preprint arXiv:1205.4779},
year = {2012}
}
Comments
7 pages