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Nov 14, 2015 at 0:24 comment added Alexandre Eremenko Also see the Wikipedia article "Hurwitz's automorphisms theorem". It has a nice discussion of the subject.
Nov 14, 2015 at 0:21 comment added Alexandre Eremenko The bounds are attained (see the references that I included). I believe that the second question is addressed in the second reference (S. Levy).
Nov 13, 2015 at 23:03 comment added SMS That's pretty interesting. Is it known whether the bounds are attained? And at the risk of sounding very vague, is it known what kind of groups could actually be isometry groups of hyperbolic surfaces?
Oct 31, 2015 at 17:30 history edited Alexandre Eremenko CC BY-SA 3.0
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Oct 31, 2015 at 17:15 history edited Alexandre Eremenko CC BY-SA 3.0
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Oct 30, 2015 at 2:44 history edited Alexandre Eremenko CC BY-SA 3.0
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Oct 30, 2015 at 2:38 history answered Alexandre Eremenko CC BY-SA 3.0