Ricci flow on a 3-manifold with positive scalar curvature

Author: 

Qian, Z

Publication Date: 

1 March 2009

Journal: 

Bulletin des Sciences Mathematiques

Last Updated: 

2020-06-03T03:00:28.56+01:00

Issue: 

2

Volume: 

133

DOI: 

10.1016/j.bulsci.2007.12.002

page: 

145-168

abstract: 

In this paper we consider Hamilton's Ricci flow on a 3-manifold with a metric of positive scalar curvature. We establish several a priori estimates for the Ricci flow which we believe are important in understanding possible singularities of the Ricci flow. For Ricci flow with initial metric of positive scalar curvature, we obtain a sharp estimate on the norm of the Ricci curvature in terms of the scalar curvature (which is not trivial even if the initial metric has non-negative Ricci curvature, a fact which is essential in Hamilton's estimates [R.S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255-306]), some L2-estimates for the gradients of the Ricci curvature, and finally the Harnack type estimates for the Ricci curvature. These results are established through careful (and rather complicated and lengthy) computations, integration by parts and the maximum principles for parabolic equations. © 2008 Elsevier Masson SAS. All rights reserved.

Symplectic id: 

148927

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article