Hyperbolic cusps with convex polyhedral boundary
type: Item
instance of: scholarly article
title: Hyperbolic cusps with convex polyhedral boundary
zbMATH Open document ID: 1179.57026
author: François Fillastre
author: Ivan Izmestiev
published in: Geometry \& Topology
publication date: 2009-03-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/0708.2666
review text: Given a hyperbolic metric with cone singularities on the 2-torus \(T^2\), such that all cone angles are less than \(2\pi\), the authors prove that this metric extends from \(T^2\times 0\) to a unique hyperbolic three dimensional cusp \(T^2\times [0,+\infty)\) with convex polyhedral boundary. Infinitesimal rigidity is also discussed. The authors consider not only smooth metrics on \(T^2\times [0,\infty)\), but also metrics having cone singularities along lines \(x\times [0,\infty)\), for \(x\) a cone point of \(T^2\). The main tool is a discrete scalar curvature functional in a polyhedral deformation space. This functional is concave and its critical points correspond to the metric. The paper gives an excellent overview of the subject, and the exposition is clear and well written
reviewed by: Joan Porti
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 53C24
zbMATH DE Number: 5530184
zbMATH Keywords: hyperbolic cusps
zbMATH Keywords: cone metrics
zbMATH Keywords: curvature functionals
MaRDI profile type: Publication
OpenAlex ID: W3105169573
arXiv ID: 0708.2666
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DOI: 10.2140/GT.2009.13.457
description: scientific article