Complex Analytic Theory of Teichmüller Spaces

  • Yoichi Imayoshi
  • Masahiko Taniguchi


We introduce a natural complex manifold structure of the Teichmüller space T(R) of a closed Riemann surface R of genus g (≧ 2), which is realized as a bounded domain in C3g-3. Furthermore, we prove that the Teichmüller modular group Mod(R) acts properly discontinuously as a group of biholomorphic automorphisms of T(R).


Riemann Surface Complex Manifold Quasiconformal Mapping Schwarzian Derivative Quasi Conformal Mapping 


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Copyright information

© Springer-Verlag Tokyo 1992

Authors and Affiliations

  • Yoichi Imayoshi
    • 1
  • Masahiko Taniguchi
    • 2
  1. 1.Department of Mathematics, College of General EducationOsaka UniversityToyonaka, Osaka 560Japan
  2. 2.Department of Mathematics, Faculty of ScienceKyoto UniversitySakyo-ku, Kyoto 606Japan

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