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arXiv · 2009.05842

Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds

Ke Feng·Huabin Ge·Bobo Hua
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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.

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Ke Feng, Huabin Ge, Bobo Hua. 2020-09-12. Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds. https://arxiv.org/abs/2009.05842

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