论文标题
组合RICCI流动和一类紧凑的3型manifolds的倍增
Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds
论文作者
论文摘要
我们证明，对于一个紧凑的3型manifold m，边界承认一个理想的三角调节t，在所有边缘至少有10个边缘，存在一个独特的完整双曲线指标，具有完全地球的边界，因此T对于M.的几何分解是同位物质的。在这种情况下，我们证明了扩展的RICCI流量会快速收敛到双曲线指数。
We prove that for a compact 3-manifold M with boundary admitting an ideal triangulation T with valence at least 10 at all edges, there exists a unique complete hyperbolic metric with totally geodesic boundary, so that T is isotopic to a geometric decomposition of M. Our approach is to use a variant of the combinatorial Ricci flow introduced by Luo [Luo05] for pseudo 3-manifolds. In this case, we prove that the extended Ricci flow converges to the hyperbolic metric exponentially fast.
