Combinatorial Ricci Flows with Applications to the Hyperbolization of Cusped 3-Manifolds
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Abstract In this paper, we adopt combinatorial Ricci flow to study the existence of hyperbolic structure on cusped 3-manifolds. The long-time existence and the uniqueness for the extended combinatorial Ricci flow are proven for general pseudo 3-manifolds. We prove that the extended combinatorial Ricci flow converges to a decorated hyperbolic polyhedral metric if and only if there exists a decorated hyperbolic polyhedral metric of zero Ricci curvature, and the flow converges exponentially fast in this case. For an ideally triangulated cusped 3-manifold admitting a complete hyperbolic metric, the flow provides an effective algorithm for finding the hyperbolic metric.
2010 ◽
Vol 21
(07)
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pp. 951-969
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2017 ◽
Vol 95
(1)
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pp. 277-304
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2019 ◽
Vol 71
(2)
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pp. 651-688
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2018 ◽
Vol 43
(10)
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pp. 1456-1484
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