Vol. 303, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Compactness theorems for 4-dimensional gradient Ricci solitons

Yongjia Zhang

Vol. 303 (2019), No. 1, 361–384

We prove compactness theorems for noncompact 4-dimensional shrinking and steady gradient Ricci solitons, respectively, satisfying: (1) every bounded open subset can be embedded in a closed 4-manifold with vanishing second homology group, and (2) are strongly κ-noncollapsed on all scales with respect to a uniform κ. These solitons are of interest because they are the only ones that can arise as finite-time singularity models for a Ricci flow on a closed 4-manifold with vanishing second homology group.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address 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:

dimension four, Ricci soliton, compactness
Mathematical Subject Classification 2010
Primary: 53C44
Received: 16 August 2018
Revised: 15 January 2019
Accepted: 4 April 2019
Published: 21 December 2019
Yongjia Zhang
Department of Mathematics
University of Minnesota
Twin Cities, MN 55414
United States