Asian Journal of Mathematics
Volume 23 (2019)
Convergence of discrete conformal geometry and computation of uniformization maps
Pages: 21 – 34
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.
polyhedral surfaces, discrete conformal geometry, uniformizations and convergences
2010 Mathematics Subject Classification
Primary 57Q15. Secondary 30F10, 30G25, 52B70.
Received 25 April 2017
Accepted 27 June 2017
Published 3 May 2019