2020/09/12 by Ke Feng, Feng, Ke, Huabin Ge +3 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2009.05842
openalex publication_date 2020/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.