Uniformization Theorem - Complex Classification

Complex Classification

Every Riemann surface is the quotient of a free, proper and holomorphic action of a discrete group on its universal covering and this universal covering is holomorphically isomorphic (one also says: "conformally equivalent") to one of the following:

  1. the Riemann sphere
  2. the complex plane
  3. the unit disk in the complex plane.

Read more about this topic:  Uniformization Theorem

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