Volume 26, issue 3 (2022)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 27
Issue 9, 3387–3831
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

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
This article is available for purchase or by subscription. See below.
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 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 (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.

PDF Access Denied

We have not been able to recognize your IP address 3.235.145.108 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
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
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