A discrete uniformization theorem for polyhedral surfaces II

@article{Gu2018ADU,
  title={A discrete uniformization theorem for polyhedral surfaces II},
  author={Xianfeng Gu and Ren Guo and Feng Luo and Jian Sun and Tianqi Wu},
  journal={Journal of Differential Geometry},
  year={2018}
}
A 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… 

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