Hyperbolic polygons and simple closed geodesics
type: Item
instance of: scholarly article
title: Hyperbolic polygons and simple closed geodesics
zbMATH Open document ID: 1114.30044
author: Hugo Parlier
published in: L'Enseignement Mathématique. 2e Série
publication date: 2007-04-10T00:00:00Z
review text: In this paper the author studies a universal constant for simple closed geodesics and the radius of a disk on closed hyperbolic Riemann surfaces by using the properties of the right-angled hyperbolic polygons. Let \(S\) be a closed Riemann surface of genus \(g>1\) with a metric of constant curvature \(-1\). Then it is proved that for every simple closed geodesic \(\gamma\) on \(S\) there exist \(4g-4\) closed disks of radius \(\frac 1 2 \ln 3\) contained in \(S\setminus \gamma\). Furthermore, if \(\rho>\frac 1 2 \ln 3\), then there exists a simple closed geodesic \(\gamma_{\rho}\) such that \(S\setminus \gamma_{\rho}\) does not contain any open disks of radius \(\rho\). The author states the result for hyperbolic Riemann surfaces of signature \((g,n)\) and Klein surfaces with respect to Marden's universal constant for Fuchsian groups.
reviewed by: Gou Nakamura
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 5141212
zbMATH Keywords: hyperbolic polygons
zbMATH Keywords: simple closed geodesics
MaRDI profile type: Publication
Recommended article: Q5421078
Recommended article: The geometry of cyclic hyperbolic polygons
Recommended article: Simple Closed Geodesics in Hyperbolic 3-Manifolds
Recommended article: Closed geodesics on doubled polygons
Recommended article: Closed geodesics on the surface of a simplex
Recommended article: Simple closed geodesics on convex surfaces
Recommended article: Q6164786
Recommended article: On the number of closed geodesics on a polyhedron
Recommended article: The geometry of hyperbolic curvoids
Recommended article: Q5320188
description: scientific article; zbMATH DE number 5141212