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May 20, 2013 at 16:31 comment added Ben McKay This approach of Thurston is similar to Kobayashi's approach in ``Projective structures with trivial intrinsic pseudodistance'', 1978, maybe earlier than Thurston? He was already working with projective connections, but in the real category rather than complex, defining a Kobayashi pseudometric.
May 20, 2013 at 14:43 comment added aglearner Dear Curtis, thank you for this remark! Have I got you correctly, that you put $U$ inside $\partial H^3$. Do you know if someone studied the definition that I propose?
May 20, 2013 at 5:30 history answered Curtis McMullen CC BY-SA 3.0