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Sep 22, 2016 at 1:55 comment added Anton Petrunin You take the doubling of triangle and pass to its covering branching at the vertices, so that the curvature becomes negative. You claim that in the obtained space a random closed geodesic does not bump into vertex with probability near 1. Did I understood you correctly? If yes, then I am surprised and I need to think.
Sep 21, 2016 at 8:07 comment added Igor Rivin @AntonPetrunin I have made similar computations a long while ago. Since the curvatures are all negative I am pretty sure this works...
Sep 21, 2016 at 1:08 comment added Anton Petrunin I do not think entropy can feel it; did you made the calculations?
Sep 20, 2016 at 22:56 history answered Igor Rivin CC BY-SA 3.0