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 
@article{AMBP_2023__30_2_189_0,
     author = {Zhipeng Lu},
     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},
     volume = {30},
     number = {2},
     year = {2023},
     doi = {10.5802/ambp.421},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.421/}
}
TY  - JOUR
AU  - Zhipeng Lu
TI  - Geodesic cover of Fuchsian groups
JO  - Annales mathématiques Blaise Pascal
PY  - 2023
SP  - 189
EP  - 199
VL  - 30
IS  - 2
PB  - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.421/
DO  - 10.5802/ambp.421
LA  - en
ID  - AMBP_2023__30_2_189_0
ER  - 
%0 Journal Article
%A Zhipeng Lu
%T Geodesic cover of Fuchsian groups
%J Annales mathématiques Blaise Pascal
%D 2023
%P 189-199
%V 30
%N 2
%I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.421/
%R 10.5802/ambp.421
%G en
%F AMBP_2023__30_2_189_0
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/

[1] Alan F. Beardon The Geometry of Discrete Groups, Graduate Texts in Mathematics, 91, Springer, 1983 | DOI | Zbl

[2] T. C. Chau A note concerning Fox’s paper on Fenchel’s conjecture, Proc. Am. Math. Soc., Volume 88 (1983), pp. 584-586 | MR | Zbl

[3] Ralph H. Fox On Fenchel’s conjecture about F-groups, Mat. Tidsskr. B (1952), pp. 61-65 | MR

[4] Toshiaki Hattori Shimizu’s lemma for classical groups, Proc. Lond. Math. Soc., Volume 117 (2018) no. 6, pp. 1281-1320 | DOI | MR | Zbl

[5] Svetlana Katok Fuchsian Groups, Chicago Lectures in Mathematics, University of Chicago Press, 1992

[6] Zhipeng Lu; Xianchang Meng Erdős distinct distances in hyperbolic surfaces (2020) | arXiv

[7] Hideo Shimizu On discontinuous groups operating on the product of the upper half planes, Ann. Math., Volume 77 (1963), pp. 33-71 | DOI | MR | Zbl

[8] Goro Shimura Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, 11, Iwanami Shoten and Princeton University Press, 1971 | Zbl

Cité par Sources :