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This is not the most precise question but rather a hope that someone has seen something like this. I am given a triangulation of the 2-sphere $S^2$ which I only know up to Moebius transformations. I ...

In this paper: http://www.dm.unipi.it/~benedett/rodin-sullivan.pdf Rodin and Sullivan show that circle packings converge to the Riemann map. Later, Scharmm and He found another proof of the same ...