论文标题
组合ricci流在刺痛的3个脉冲上
Combinatorial Ricci flow on cusped 3-manifolds
论文作者
论文摘要
组合ricci在cused $ 3 $ -manifold上流动是Chow-luo的组合Ricci在表面上流动的类似物，而Luo的组合Ricci在紧凑型$ 3 $ manifolds上流动与边界的边界上，以寻找在cuseped $ 3 $ -MANIFOLDS上找到完整的超质量衡量。 Casson和Rivin最大化角度结构体积的计划，组合RICCI流程通过最大程度地减少装饰双曲线多边性指标的共同数量，从而在$ 3 $ MANIFOLD上找到了完整的双曲线度量。组合RICCI流程可能会产生奇异性。我们通过使用Lu-Yang的扩展来扩展流经潜在的奇异性来克服这一困难。结果表明，在cused $ 3 $ - manifold上存在一个完整的双曲线度量，相当于扩展的组合RICCI流的融合，这给了Casson and Rivin和Rivin的程序的3美元的$ 3 $ manifold dual $ 3 $ manifold dual，这给出了新的表征。扩展的组合RICCI流还提供了一种有效的算法，可在损失$ 3 $ manifolds上查找完整的双曲线指标。
Combinatorial Ricci flow on a cusped $3$-manifold is an analogue of Chow-Luo's combinatorial Ricci flow on surfaces and Luo's combinatorial Ricci flow on compact $3$-manifolds with boundary for finding complete hyperbolic metrics on cusped $3$-manifolds. Dual to Casson and Rivin's program of maximizing the volume of angle structures, combinatorial Ricci flow finds the complete hyperbolic metric on a cusped $3$-manifold by minimizing the co-volume of decorated hyperbolic polyhedral metrics. The combinatorial Ricci flow may develop singularities. We overcome this difficulty by extending the flow through the potential singularities using Luo-Yang's extension. It is shown that the existence of a complete hyperbolic metric on a cusped $3$-manifold is equivalent to the convergence of the extended combinatorial Ricci flow, which gives a new characterization of existence of a complete hyperbolic metric on a cusped $3$-manifold dual to Casson and Rivin's program. The extended combinatorial Ricci flow also provides an effective algorithm for finding complete hyperbolic metrics on cusped $3$-manifolds.
