Volume 23, issue 7 (2019)

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

Volume 24, 1 issue

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
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature

Antoine Song

Geometry & Topology 23 (2019) 3501–3535
Abstract

We construct spherical space forms (S3Γ,g) with positive scalar curvature and containing no stable embedded minimal surfaces such that the following happens along the Ricci flow starting at (S3Γ,g): a stable embedded minimal 2–sphere appears and a nontrivial singularity occurs. We also give in dimension 3 a general construction of Type I neckpinching and clarify the relationship between stable spheres and nontrivial Type I singularities of the Ricci flow. Some symmetry assumptions prevent the appearance of stable spheres, and this has consequences on the types of singularities which can occur for metrics with these symmetries.

Keywords
Ricci flow, minimal spheres, scalar curvature
Mathematical Subject Classification 2010
Primary: 53A10, 53C44
References
Publication
Received: 3 May 2018
Revised: 8 January 2019
Accepted: 9 January 2019
Published: 30 December 2019
Proposed: John Lott
Seconded: Ian Agol, Bruce Kleiner
Authors
Antoine Song
Department of Mathematics
Princeton University
Princeton, NJ
United States