The distance between different components of the universal Teichmüller space
type: Item
instance of: scholarly article
title: The distance between different components of the universal Teichmüller space
zbMATH Open document ID: 1085.30043
DOI: 10.1142/S0252959905000427
author: Zhe Wang
published in: Chinese Annals of Mathematics. Series B
publication date: 2006-02-22T00:00:00Z
review text: In this paper the author considers a class of maps. The model of the universal Teichmüller space considered by the author in this paper is the set of conformal maps \(f\) defined on the disc with \(f(0)=0\), \(f'(0)=1\) and possessing a quasi-conformal extension to the Riemann sphere. One considers the norm \(\sup (1-| z| ^{2}) | f''(z)/f'(z)| \) where the supremum is taken over the unit disc. It has been shown by \textit{I. V. Zhuravlev} [``Model of the universal Teichmüller space'', Sib. Math. J. 27, 691--697 (1986); translation from Sib. Mat. Zh. 27, No. 5 (159), 75--82 (1986; Zbl 0616.30023)] that in the induced topology the universal Teichmüller space is disconnected and one can describe the components. Moreover one can construct for each component a special element called here the \textit{centre}. The author shows here that the distance between any two components is zero and that the distance between the centres of two distinct components is 2.
Mathematics Subject Classification ID: 30F60
zbMATH DE Number: 5008960
zbMATH Keywords: universal Teichmüller space
zbMATH Keywords: Schwarzian derivative
zbMATH Keywords: quasi-conformal extension
zbMATH Keywords: logarithmic derivative
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
Recommended article: Teichmüller distance and Kobayashi distance on subspaces of the universal Teichmüller space
Recommended article: Q4458798
Recommended article: Q3704188
Recommended article: Distance and angles between Teichmüller geodesics
Recommended article: The Teichmüller distance on the space of flat conformal structures
Recommended article: Q4508511
Recommended article: The Teichmüller distance on the space of spherical CR structures
Recommended article: Q4679746
Recommended article: Q4285878
description: scientific article; zbMATH DE number 5008960