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Combinatorial Ricci flows
and the hyperbolization of a class of compact
$3$–manifolds
Ke Feng, Huabin Ge and Bobo Hua |
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Geometry & Topology 26 (2022) 1349–1384
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Abstract |
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We prove that for a compact –manifold with boundary admitting an ideal triangulation with valence at least 10 at all edges, there exists a unique complete hyperbolic metric with totally geodesic boundary, so that is isotopic to a geometric decomposition of . Our approach is to use a variant of the combinatorial Ricci flow introduced by Luo (Electron. Res. Announc. Amer. Math. Soc. 11 (2005) 12–20) for pseudo-–manifolds. In this case, we prove that the extended Ricci flow converges to the hyperbolic metric exponentially fast. |
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Keywords
Ricci flow, hyperbolization, 3–manifold, ideal
triangulation, hyperbolic metric
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Mathematical Subject Classification
Primary: 05E45, 53E20, 57K32, 57M50, 57Q15
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References |
Publication
Received: 6 October 2020
Revised: 7 March 2021
Accepted: 23 April 2021
Published: 3 August 2022
Proposed: David Gabai
Seconded: John Lott, Tobias H Colding
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Authors |
| Ke Feng | |
| School of Mathematical
Sciences University of Electronic Science and Technology of China Chengdu Sichuan China |
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| Huabin Ge | |
| School of Mathematics Renmin University of China Beijing China |
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| Bobo Hua | |
| School of Mathematical Sciences,
LMNS Fudan University Shanghai China |
Shanghai Center for Mathematical
Sciences Fudan University Shanghai China |
