Volume maximization and the extended hyperbolic space
type: Item
instance of: scholarly article
title: Volume maximization and the extended hyperbolic space
zbMATH Open document ID: 1250.57028
DOI: 10.1090/S0002-9939-2011-10941-9
author: Feng Luo
author: Jean-Marc Schlenker
published in: Proceedings of the American Mathematical Society
publication date: 2012-04-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/0908.2023
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 52B70
Mathematics Subject Classification ID: 57Q15
zbMATH DE Number: 6024113
zbMATH Keywords: volume functional
zbMATH Keywords: angle structure
zbMATH Keywords: de Sitter space
MaRDI profile type: Publication
arXiv ID: 0908.2023
cites work: VOLUME OF C1,α-BOUNDARY DOMAIN IN EXTENDED HYPERBOLIC SPACE
cites work: Triangulations in Mobius Geometry
cites work: Volume and angle structures on 3-manifolds
cites work: Q4877326
cites work: Metrics on hyperbolic convex polyhedra
cites work: Convex polyhedra in Lorentzian space-forms
cites work: Q3062972
OpenAlex ID: W1969312689
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review text: Given an angle structure on a triangulation of a 3-manifold, Casson-Rivin (for a 3-manifold with torus boundary) and Luo (for closed 3 manifolds) defined a naturally associated hyperbolic volume.NEWLINENEWLINEIn the paper under review, the authors investigate the relationship between the critical points of the volume functional and a natural extension of hyperbolic space by de Sitter space. They show that many of the critical points have geometric meaning (e.g. the existence of a spherical metric) in terms of geometric structures based on the extended hyperbolic space.
reviewed by: Mahan Mj
description: scientific article; zbMATH DE number 6024113