#### Volume 26, issue 3 (2022)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Combinatorial Ricci flows and the hyperbolization of a class of compact $3$–manifolds

### Ke Feng, Huabin Ge and Bobo Hua

Geometry & Topology 26 (2022) 1349–1384
##### Abstract

We prove that for a compact $3$–manifold $M$ with boundary admitting an ideal triangulation $\mathsc{𝒯}$ with valence at least 10 at all edges, there exists a unique complete hyperbolic metric with totally geodesic boundary, so that $\mathsc{𝒯}$ is isotopic to a geometric decomposition of $M\phantom{\rule{-0.17em}{0ex}}$. 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-$3$–manifolds. In this case, we prove that the extended Ricci flow converges to the hyperbolic metric exponentially fast.

We have not been able to recognize your IP address 44.200.171.156 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

##### Keywords
Ricci flow, hyperbolization, 3–manifold, ideal triangulation, hyperbolic metric
##### Mathematical Subject Classification
Primary: 05E45, 53E20, 57K32, 57M50, 57Q15
##### 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
##### Authors
 Ke Feng School of Mathematical Sciences University of Electronic Science and Technology of China Chengdu Sichuan China Huabin Ge School of Mathematics Renmin University of China Beijing China Bobo Hua School of Mathematical Sciences, LMNS Fudan University Shanghai China Shanghai Center for Mathematical Sciences Fudan University Shanghai China