A discrete uniformization theorem for polyhedral surfaces II
A discrete uniformization theorem for polyhedral surfaces II
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DOI：
10.4310/jdg/1531188190
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发表时间：
2014-01
影响因子：
2.5
通讯作者：
X. Gu;Ren Guo;F. Luo;Jian Sun;Tianqi Wu
中科院分区：
文献类型：
--
作者：
X. Gu;Ren Guo;F. Luo;Jian Sun;Tianqi Wu
引入了双曲多面体曲面的离散保形性。这种离散保形性被证明是可计算的。证明了闭曲面上的每个双曲多面体度量都离散共形于唯一的双曲多面体度量，且该度量的离散曲率满足Gauss-Bonnet公式。此外，具有给定曲率的双曲多面体度量可以通过外科手术的离散Yamabe流来获得。特别地，具有负欧拉特征的闭曲面上的每个双曲多面体度量都离散共形于唯一的双曲度量。
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.