论文标题
组合ricci流动与Cusped 3-manifolds的倍增
Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds
论文作者
论文摘要
在本文中，我们采用组合RICCI曲率流量方法来研究在具有圆环边界的3个manifolds上的双曲线结构的存在。对于一般的伪3个manifolds，我们证明了长期存在和延长的RICCI流量的独特性，用于装饰双曲线多面体指标。我们证明，当且仅当存在零RICCI曲率的装饰双曲线多面体度量时，且仅当存在时，延伸的RICCI流就会收敛到装饰的双曲线多面体度量。如果是这种情况，则流量会迅速收敛。这些结果适用于通过理想的三角剖分在3个manifolds上的双曲线结构。
In this paper, we adopt combinatorial Ricci curvature flow methods to study the existence of cusped hyperbolic structure on 3-manifolds with torus boundary. For general pseudo 3-manifolds, we prove the long-time existence and the uniqueness for the extended Ricci flow for decorated hyperbolic polyhedral metrics. We prove that the extended Ricci flow converges to a decorated hyperbolic polyhedral metric if and only if there exists a decorated hyperbolic polyhedral metric of zero Ricci curvature. If it is the case, the flow converges exponentially fast. These results apply for cusped hyperbolic structure on 3-manifolds via ideal triangulation.
