On the horoboundary and the geometry of rays of negatively curved manifolds
type: Item
instance of: scholarly article
title: On the horoboundary and the geometry of rays of negatively curved manifolds
zbMATH Open document ID: 1260.53068
author: Françoise Dal'Bo
author: Marc Peigné
author: Andrea Sambusetti
published in: Pacific Journal of Mathematics
publication date: 2012-11-21T00:00:00Z
full work available at URL: p03.xhtml
review text: The authors study the Gromov boundary of quotients \(X/\Gamma\) of a Hadamard space \(X\) by an infinite group \(\Gamma\) of isometries. The authors describe some hyperbolic surfaces with infinite fundamental group whose Gromov boundaries exemplify some of the pathologies that can arise. These include divergent rays with equal Busemann functions, points on the Gromov boundary not corresponding to Busemann functions, and the discontinuity of Busemann functions as functions of the initial point and direction of a ray. For a certain class of such quotients \(X/\Gamma\), known as geometrically finite, the authors prove that the Gromov compactification has only conical singularities.
reviewed by: Benjamin McKay
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 57S30
zbMATH DE Number: 6109303
zbMATH Keywords: Gromov boundary
zbMATH Keywords: horofunction
zbMATH Keywords: geometrically finite
zbMATH Keywords: asymptotic ray
MaRDI profile type: Publication
OpenAlex ID: W2949112369
Wikidata QID: Q64438067
DOI: 10.2140/PJM.2012.259.55
description: scientific article; zbMATH DE number 6109303