A discrete conformality for polyhedral metrics on surfaces is introduced in this paper. It is shown that each polyhedral metric on a compact surface is discrete conformal to a constant curvature polyhedral metric which is unique up to scaling. Furthermore, the constant curvature metric can be found using a finite dimensional variational principle.
"A discrete uniformization theorem for polyhedral surfaces." J. Differential Geom. 109 (2) 223 - 256, June 2018. https://doi.org/10.4310/jdg/1527040872