Convergence of discrete conformal geometry and computation of uniformization maps
Convergence of discrete conformal geometry and computation of uniformization maps
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DOI：
10.4310/ajm.2019.v23.n1.a2
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发表时间：
2019
影响因子：
0.6
通讯作者：
D. Gu;F. Luo;Tianqi Wu
中科院分区：
文献类型：
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作者：
D. Gu;F. Luo;Tianqi Wu
庞加莱和柯比的经典均匀化定理指出，任何具有黎曼度规的单连通曲面都与黎曼球、复平面或单位盘共形微分同态。利用guu - luo - sun - wu[9]在多面体曲面的离散共形几何上的工作，我们证明了单连通黎曼曲面的均匀化映射是可计算的。
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 [9] on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.