Teichmüller Spaces

Yoichi Imayoshi and Masahiko Taniguchi
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Yoichi Imayoshi: Osaka University, Department of Mathematics, College of General Education
Masahiko Taniguchi: Kyoto University, Department of Mathematics, Faculty of Science

Chapter Chapter 5 in An Introduction to Teichmüller Spaces, 1992, pp 119-145 from Springer

Abstract: Abstract In this chapter, we shall construct Teichmüller spaces alternatively by using quasiconformal mappings. First, in Section 1, we give a new definition of the Teichmüller space of an arbitrary Riemann surface by using quasiconformal mappings. In Sections 2 and 3, we investigate the case of closed Riemann surfaces of genus g (≥ 2), and prove Teichmüller’s theorem, which states that the Teichmüller space of a closed Riemann surface of genus g (≥ 2) is homeomorphic to the open unit ball in the real (6g – 6)-dimensional Euclidean space. The key of the proof is the existence and uniqueness of the extremal quasiconformal mappings, called Teichmüller mappings.

Keywords: Riemann Surface; Conformal Mapping; Quasiconformal Mapping; Fuchsian Group; Quasi Conformal Mapping (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68174-8_5

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DOI: 10.1007/978-4-431-68174-8_5

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