Annales Mathématiques
Blaise Pascal
no. 2
Geodesic cover of Fuchsian groups
Zhipeng Lu1
1 Shenzhen MSU-BIT University & Guangdong Laboratory of Machine Perception and Intelligent Computing Shenzhen, Guangdong 518172, China
Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 2, pp. 189-199.

We study unions of fundamental domains of a Fuchsian group, especially those with hyperbolic plane metric realizing the metric of the corresponding hyperbolic surface. We call these unions the geodesic covers of the Fuchsian group or the hyperbolic surface. The paper contributes to showing that finiteness of geodesic covers is basically another characterization of geometrically finiteness. The resolution of geometrically finite case is based on Shimizu’s lemma.

Publié le :
DOI : 10.5802/ambp.421
Classification : 05A16, 05C88, 05C89
Mots clés : Fuchsian groups, geometrically finite, infinitely generated

Zhipeng Lu 1

1 Shenzhen MSU-BIT University & Guangdong Laboratory of Machine Perception and Intelligent Computing Shenzhen, Guangdong 518172, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Zhipeng Lu. Geodesic cover of Fuchsian groups. Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 2, pp. 189-199. doi : 10.5802/ambp.421. https://ambp.centre-mersenne.org/articles/10.5802/ambp.421/

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