Inclusion relations between the Bers embeddings of Teichmüller spaces
type: Item
instance of: scholarly article
title: Inclusion relations between the Bers embeddings of Teichmüller spaces
zbMATH Open document ID: 1056.30046
DOI: 10.1007/BF02786628
author: Katsuhiko Matsuzaki
published in: Israel Journal of Mathematics
publication date: 2004-11-11T00:00:00Z
review text: In this paper the author considers infinite-dimensional Teichmüller spaces, that is, Teichmüller spaces of non-finitely generated Fuchsian groups. The author first introduces a notion of ``exceptional groups'', that are groups where there are additional symmetries of the space of integrable holomorphic differentails. He is able to classify all such groups and then uses this result to show that for non-exceptional groups the Fuchsian group is uniquely determined by its Bers' embedding. The proof uses Teichmüller theory and a theorem of \textit{V. Markovic} [``Biholomorphic maps between Teichmüller spaces'', Duke Math. J. 120, No. 2, 405--431 (2003; Zbl 1056.30046)].
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 2114395
zbMATH Keywords: Teichmüller theory
zbMATH Keywords: Bers' embedding
zbMATH Keywords: quadratic differentials
zbMATH Keywords: Fuchsian groups
zbMATH Keywords: exceptional Riemann surfaces
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
cites work: On the Boundedness of Automorphic Forms
cites work: Geometric Isomorphisms between Infinite Dimensional Teichmüller Spaces
cites work: Q4934580
cites work: Q4517817
cites work: Q3766016
cites work: Q5666814
cites work: An isometry theorem for quadratic differentials on Riemann surfaces of finite genus
cites work: Biholomorphic maps between Teichmüller spaces
cites work: Q3338499
description: scientific article; zbMATH DE number 2114395