Geodesic cover of Fuchsian groups

2021/04/08 by Zhipeng Lu, Lu, Zhipeng
Mathematics · #11P21 #20H10 #52C10 #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.CO #math.GT #msc:11P21 #msc:20H10 #msc:52C10

paper · pdf · doi:10.48550/arxiv.2104.04028

All comments are welcome!

arxiv created 2021/04/08 · openalex publication_date 2021/04/08 · arxiv updated 2021/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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