Complex Analytic Theory of Teichmüller Spaces
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).
KeywordsRiemann Surface Complex Manifold Quasiconformal Mapping Schwarzian Derivative Quasi Conformal Mapping
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