On the displacement of generators of free Fuchsian groups

Yan Mary He

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arXiv · 1706.09069

On the displacement of generators of free Fuchsian groups

Yan Mary He

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Abstract

We prove an inequality that must be satisfied by displacement of generators of free Fuchsian groups, which is the two-dimensional version of the $\log (2k-1)$ Theorem for Kleinian groups due to Anderson-Canary-Culler-Shalen. As applications, we obtain quantitative results on the geometry of hyperbolic surfaces such as the two-dimensional Margulis constant and lengths of closed curves, which improves a result of Buser's.

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Yan Mary He. 2017-06-27. On the displacement of generators of free Fuchsian groups. https://arxiv.org/abs/1706.09069

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