Asymptotic behavior of flat surfaces in hyperbolic 3-space

Details Asymptotic behavior of flat surfaces in hyperbolic 3-space Asymptotic behavior of flat surfaces in hyperbolic 3-space

2007-08-02

arxiv.org/abs/0708.0300v3

J. Math. Soc. Japan 61(3), 2009, 799-852

Mathematics

Differential Geometry

34 pages, 6 figures

Scientific paper

In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic 3-space H^3. Galvez, Martinez and Milan showed that when the singular set does not accumulate at an end, the end is asymptotic to a rotationally symmetric flat surface. As a refinement of their result, we show that the asymptotic order (called "pitch" p) of the end determines the limiting shape, even when the singular set does accumulate at the end. If the singular set is bounded away from the end, we have -1

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