A discrete uniformization theorem for polyhedral surfaces II

By Xianfeng David Gu, Ren Guo, Feng Luo, Jian Sun, Tianqi Wu. Journal of differential geometry, 2014

131 citations recorded by the source corpus.

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 polyhedral metric on a closed surface with negative Euler characteristic is discrete conformal to a unique hyperbolic metric.

Subfields: Applied Mathematics, Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c5c2d1288bcfaba888c09fda13fa73a50b4f34a4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Xianfeng David Gu
2. Tianqi Wu
3. Jian Sun
4. Feng Luo
5. David Glickenstein
6. Xu Xu
7. Huabin Ge
8. Boris A. Springborn

In Computational Mechanics

1. Feng Luo
2. Xianfeng David Gu
3. Bruno Lévy

In Geometry and Topology

1. Xianfeng David Gu
2. Tianqi Wu
3. Jian Sun
4. Feng Luo
5. David Glickenstein
6. Xu Xu

Citations in the corpus

• A discrete uniformization theorem for polyhedral surfaces (2013, background): “2 for hyperbolic polyhedral metrics on (S, V ) has been proved in [21] which is a sequel to the current paper.”