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May 13, 2014 at 23:43 vote accept Pablo Lessa
May 12, 2014 at 21:29 comment added Pablo Lessa Thanks! Maskit's work is relevant. He gives upper and lower bounds on the quotient of the extremal length the free homotopy class of a closed geodesic and hyperbolic length of the geodesic on a closed hyperbolic surface. In particular they go to zero and infinity together (though at infinity the quotient might be unbounded).
May 12, 2014 at 17:00 history answered Dylan Thurston CC BY-SA 3.0