The Canonical Metric on a Riemann Surface and Its Induced Metric on Teichmüller Space
نویسنده
چکیده
Throughout this paper Σ is a smooth, oriented, closed Riemann surface of genus g, with n punctures and 3g−3+n > 1. Teichmüller space Tg,n is the space of conformal structures on Σ, where two conformal structures σ and ρ are equivalent if there is a biholomorphic map between (Σ, σ) and (Σ, ρ) in the homotopy class of the identity map. The moduli space Mg of Riemann surfaces can be obtained as the quotient of Teichmüller space by the mapping class group.
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