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Can somebody give me the sketch of the proof of the uniformization theorem, given that every compact Riemann surface admits a non-constant meromorphic function. (I am not so sure these two are indeed related or not.)

I just want to know how the story goes on.

Mike Park
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  • Here's a similar question on MO: https://mathoverflow.net/questions/10516/uniformization-theorem-for-riemann-surfaces – Hans Lundmark Aug 20 '18 at 14:02
  • Actually I already read the answers on the link, but I want some more details, the overall outline of the proof. – Mike Park Aug 22 '18 at 04:06

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