Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds
Differential Geometry
2022-08-17 v2 Algebraic Topology
Geometric Topology
Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2009.03731,
title = {Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds},
author = {Ke Feng and Huabin Ge and Bobo Hua},
journal= {arXiv preprint arXiv:2009.03731},
year = {2022}
}
Comments
31 pages. This is a revision of the paper