Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory
type: Item
instance of: scholarly article
title: Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory
zbMATH Open document ID: 1279.32012
author: G. Théret
author: Athanase Papadopoulos
published in: Geometriae Dedicata
publication date: 2012-11-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1001.2088
review text: On the Teichmüller space of a hyperbolic surface of finite type, Thurston has introduced an asymmetric metric and studied a class of geodesics for this metric called stretch lines. In the paper under review the authors construct some special stretch lines that are also geodesic lines (up to reparametrization) for Thurston's asymmetric metric when traversed in the reverse direction. These lines are directed by complete geodesic laminations that are not chain-recurrent and have a nice description in terms of the Fenchel-Nielsen coordinates.
reviewed by: Yuliang Shen
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30F30
Mathematics Subject Classification ID: 30F60
zbMATH DE Number: 6111329
zbMATH Keywords: Teichmüller space
zbMATH Keywords: hyperbolic surface
zbMATH Keywords: Thurston's asymmetric metric
zbMATH Keywords: stretch line
MaRDI profile type: Publication
OpenAlex ID: W2020192872
arXiv ID: 1001.2088
cites work: Comparison between Teichmüller and Lipschitz metrics
cites work: On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary
cites work: Q3592881
cites work: Shift coordinates, stretch lines and polyhedral structures for Teichmüller space
cites work: Shortening all the simple closed geodesics on surfaces with boundary
cites work: Q4337982
DOI: 10.1007/S10711-012-9694-4
description: scientific article