Journal of Differential Geometry
- J. Differential Geom.
- Volume 109, Number 3 (2018), 431-466.
A discrete uniformization theorem for polyhedral surfaces II
A notion of discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying Gauss–Bonnet formula. Furthermore, the hyperbolic polyhedral metric with given curvature can be obtained using a discrete Yamabe flow with surgery. In particular, each hyperbolic polyhedral metric on a closed surface with negative Euler characteristic is discrete conformal to a unique hyperbolic metric.
J. Differential Geom., Volume 109, Number 3 (2018), 431-466.
Received: 16 April 2014
First available in Project Euclid: 10 July 2018
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Gu, Xianfeng; Guo, Ren; Luo, Feng; Sun, Jian; Wu, Tianqi. A discrete uniformization theorem for polyhedral surfaces II. J. Differential Geom. 109 (2018), no. 3, 431--466. doi:10.4310/jdg/1531188190. https://projecteuclid.org/euclid.jdg/1531188190