On analytic and geometric properties of Teichmüller spaces
type: Item
instance of: scholarly article
title: On analytic and geometric properties of Teichmüller spaces
zbMATH Open document ID: 0591.32027
author: Hiroshige Shiga
published in: Journal of Mathematics of Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: The work is devoted to application of methods of the geometric theory of functions to the theory of Teichmüller spaces. In the first part, the author develops and improves the results of \textit{I. V. Zhuravlev} [Sov. Math., Dokl. 21, 252-255 (1980); translation from Dokl. Akad. Nauk SSSR 250, 1047-1050 (1980; Zbl 0467.30037)]. The obtained results are used for a new proof of the theorem of \textit{W. Abikoff} [Ann. Math. Stud. 97, 3-5 (1981; Zbl 0458.30031)] on the structure of the boundary of a Teichmüller space, a new proof of the results of \textit{S. L. Krushkal'} [Sov. Math., Dokl. 17, 704-707 (1976); translation from Dokl. Akad. Nauk SSSR 228, 290-292 (1976; Zbl 0347.32011)] and these of \textit{I. Kra} [Lect. Notes Math. 747, 230-241 (1979; Zbl 0422.32018)] on completeness of the Teichmüller metric. The second part of the work is devoted to the study of boundary behaviour of holomorphic mappings of a unit disc into the Teichmüller space. In the third part, the boundary behaviour of the first kind holomorphic differentials as functions on the Teichmüller space are studied.
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 32E35
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 30F30
zbMATH DE Number: 3948731
zbMATH Keywords: Teichmüller spaces
zbMATH Keywords: completeness of the Teichmüller metric
zbMATH Keywords: boundary behaviour of holomorphic mappings
zbMATH Keywords: holomorphic differentials
reviewed by: Alexander Mednykh
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521274
OpenAlex ID: W1501366435
DOI: 10.1215/KJM/1250521274
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description: scientific article; zbMATH DE number 3948731