The ideal Thurston-Andreev theorem and triangulation production
  This paper contains a generalization of the convex ideal case of the Thurston-Andreev theorem when the genus is greater than 1. The heart of the paper concerns taking formal angle data on a surface and ``conformally flowing'' this formal angle data to uniquely associated uniform angle data. This flow turns out to be the gradient of an objective function related in a rather magical way to hyperbolic volume. 
Gregory Leibon (Dartmouth)