On volumes of hyperbolic orbifolds
type: Item
instance of: scholarly article
title: On volumes of hyperbolic orbifolds
zbMATH Open document ID: 1255.57015
author: Ilesanmi Adeboye
author: Guofang Wei
published in: Algebraic \& Geometric Topology
publication date: 2012-05-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/0911.4712
review text: Lower bounds for the radius \(r_{n}\) of the largest ball that can be embedded in any hyperbolic \(n\)-manifold (and, hence, lower bounds on the volumes of these spaces) have been known for some time [\textit{G. J. Martin}, J. Lond. Math. Soc., II. Ser. 40, No. 2, 257--264 (1989; Zbl 0709.30040)]. In this paper, the authors prove that the volume of a hyperbolic \(n\)-orbifold is bounded below by a constant (an explicit formula for which is computed) that depends only on the dimension of the orbifold. This significantly improves upon the above volume bounds for manifolds, as well as on previous work of the first author [\textit{I. Adeboye}, Pac. J. Math. 237, No. 1, 1--19 (2008; Zbl 1149.57026)]. In the cases when \(n\) equals either 2 or 3, the authors refine the estimates to produce better bounds than those given by the general formula. The proof of the result uses a bound developed by Wang [\textit{H.-C. Wang}, J. Differ. Geom. 3, 481--492 (1969; Zbl 0197.30403)] on the radius of a ball embedded in the fundamental domain of a lattice of a semisimple Lie group.
reviewed by: Shawn Rafalski
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57N16
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 6035475
zbMATH Keywords: hyperbolic orbifold
zbMATH Keywords: volume
MaRDI profile type: Publication
OpenAlex ID: W1981486635
arXiv ID: 0911.4712
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DOI: 10.2140/AGT.2012.12.215
description: scientific article; zbMATH DE number 6035475