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Jul 16, 2014 at 15:38 comment added Lee Mosher Ah, you're right, I have still missed the main point, which is to pick a continuously varying family of diffeomorphisms from a base hexagon $Q(x_0,y_0,z_0)$ to each of the other hexagons in this family…….
Jul 16, 2014 at 15:29 comment added Pablo Lessa As far as I can tell you're showing that the Teichmuller space is in fact $(\mathbb{R}^+)^3$. But how does this give you a smooth Riemannian metric on $P$ varying continuously (in the smooth topology) with respect to $x,y,z$?
Jul 16, 2014 at 15:23 history answered Lee Mosher CC BY-SA 3.0