Geodesic
Geodesic cover of Fuchsian groups
Lu, Zhipeng1
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

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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
Keywords: Fuchsian groups, geometrically finite, infinitely generated

Lu, Zhipeng 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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     title = {Geodesic cover of {Fuchsian} groups},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {189--199},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
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Lu, Zhipeng. Geodesic cover of Fuchsian groups. Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 2, pp. 189-199. doi: 10.5802/ambp.421

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