Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds
Differential Geometry
2020-09-15 v1 Geometric Topology
Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2009.05842,
title = {Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds},
author = {Ke Feng and Huabin Ge and Bobo Hua},
journal= {arXiv preprint arXiv:2009.05842},
year = {2020}
}