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Hyperbolic structures on infinite type surfaces

Let S be a surface whose fundamental group is NOT finitely generated. Does there exist a complete hyperbolic metric on S for which the area is finite? I suspect the answer in general is NO, but I do n …
Ferran V.'s user avatar
  • 637
7 votes

Translation surfaces

People normally take the definition: translation surface = pair (X,w), where X is Riemann Surface and w is a non identically zero holomorphic form on X. Strictly, if you want to make a translation sur …
Ferran V.'s user avatar
  • 637