Closed geodesics on ideal polyhedra of dimension 2
type: Item
instance of: scholarly article
title: Closed geodesics on ideal polyhedra of dimension 2
zbMATH Open document ID: 0869.52003
author: Charalampos Charitos
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-11-12T00:00:00Z
full work available at URL: CONT26-2.html
review text: Ideal polyhedra of dimension 2 are unions of ideal hyperbolic triangles which are glued together by isometries along their sides. The infimum of the lengths of broken geodesics defines a pseudodistance on such ideal polyhedra. In Theorem 1 the author proves that this is in fact a geodesic metric under certain finiteness assumptions. In Theorem 2 it is shown that for each closed curve there is a unique distance realizing closed geodesic in the same homotopy class. The only exception are curves homotopic to a cusp, meaning that the infimum of the length in this homotopy class is zero. However, this minimal closed geodesic is not necessarily simple.
Mathematics Subject Classification ID: 52A55
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 944405
zbMATH Keywords: developing surface
zbMATH Keywords: geodesic segment
zbMATH Keywords: ideal triangle
zbMATH Keywords: ideal polyhedron
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
OpenAlex ID: W2027959388
cites work: Q4865842
cites work: Shortening curves on surfaces
cites work: Q4747183
cites work: Q3827546
cites work: Q4865841
DOI: 10.1216/RMJM/1181072071
description: scientific article; zbMATH DE number 944405