On the minimal distance between elliptic fixed points for geometrically finite Fuchsian groups (Q2816461)
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scientific article; zbMATH DE number 6618765
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the minimal distance between elliptic fixed points for geometrically finite Fuchsian groups |
scientific article; zbMATH DE number 6618765 |
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On the minimal distance between elliptic fixed points for geometrically finite Fuchsian groups (English)
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22 August 2016
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Fuchsian groups
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elliptic elements
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elementary groups
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hyperbolic distance
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Let \(\Gamma\subset \text{PSL}(2,\mathbb{R})\) be a cofinite Fuchsian group and \({\mathcal E}\) be the set of the elliptic fixed points in the upper half plane. If \(\ell_0\) in the length of the smallest closed geodesic on \(\mathbb{H}/\Gamma\) then \(d(z_1,z_2)\geq \min\{{\ell_0\over 2},\;0.151\}\) for the hyperbolic distance of two different \(z_1,z_2\in{\mathcal E}\). The proofs are elementary and easy to read.
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0.7673758268356323
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0.7673758268356323
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0.741113543510437
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0.7284381985664368
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