The classical uniformization theorem of Poincaré and Koebe states that any simply connected surface with a Riemannian metric is conformally diffeomorphic to the Riemann sphere, or the complex plane or the unit disk. Using the work by Gu-Luo-Sun-Wu  on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Discrete conformal geometry
- Polyhedral surfaces
- Uniformizations and convergences