Outradii of the Teichmüller spaces of Fuchsian groups of the second kind
type: Item
instance of: scholarly article
title: Outradii of the Teichmüller spaces of Fuchsian groups of the second kind
zbMATH Open document ID: 0658.30037
author: Hisao Sekigawa
author: Hiro-O Yamamoto
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1986-01-01T00:00:00Z
review text: Under the Bers embedding, the Teichmüller space T(\(\Gamma)\) of a Fuchsian group \(\Gamma\) is embedded as bounded subset of a Banach space. The outradius 0(\(\Gamma)\) is \(\sup \| \phi \|\), \(\phi\in T(\Gamma)\). It is well-known that \(2<0(\Gamma)\leq 6\) and the authors have proved that \(0(\Gamma)<6\) if \(\Gamma\) is finitely-generated of the first kind [the first author, Tôhoku Math. J., II. Ser. 30, 607-612 (1978; Zbl 0398.30038)] and \(0(\Gamma)=6\) if \(\Gamma\) is finitely-generated of the second kind [the authors, J. Math. Kyoto Univ. 26, 3-30 (1986; Zbl 0603.30054)]. Here, they prove \(0(\Gamma)=6\) for all groups of the second kind, independent of the previous proof.
Mathematics Subject Classification ID: 30F99
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 4075493
zbMATH Keywords: Fuchsian group
reviewed by: C. Maclachlan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228449
OpenAlex ID: W2028976369
cites work: Q5512337
cites work: Riemann's mapping theorem for variable metrics
cites work: On boundaries of Teichmüller spaces and on Kleinian groups. I
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cites work: On holomorphic cross-sections in Teichmüller spaces
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cites work: Outradii of Teichmüller spaces of finitely generated Fuchsian groups of the second kind
DOI: 10.2748/TMJ/1178228449
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description: scientific article; zbMATH DE number 4075493