Grunsky's inequality and its applications to Teichmüller spaces
type: Item
instance of: scholarly article
title: Grunsky's inequality and its applications to Teichmüller spaces
zbMATH Open document ID: 0794.30038
author: Hiroshige Shiga
author: Harumi Tanigawa
published in: Kodai Mathematical Journal
publication date: 1994-04-28T00:00:00Z
review text: In this paper, we discuss the equality between invariant quantities, such as the Teichmüller distance and the Carathéodory distance, in Teichmüller spaces. We shall give some conditions under which these quantities are the same at some points. Examples of Fuchsian groups will be constructed in relation to the conditions above. In particular, we shall construct a Teichmüller disk in \(T(1)\) determined by a quadratic differential with a simple zero where the Teichmüller distance and the Carathéodory distance are the same. We also give an estimate of the variation of critical exponent quasi-Fuchsian groups in terms of Grunsky coefficients.
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30F35
zbMATH DE Number: 558884
zbMATH Keywords: Teichmüller distance
zbMATH Keywords: Carathéodory distance
zbMATH Keywords: quasi-Fuchsian groups
zbMATH Keywords: Grunsky coefficients
reviewed by: Steffen Timmann
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039846
OpenAlex ID: W2022049069
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DOI: 10.2996/KMJ/1138039846
description: scientific article; zbMATH DE number 558884