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Estimating the trace-free Ricci tensor in Ricci flow

Author: Dan Knopf
Journal: Proc. Amer. Math. Soc. 137 (2009), 3099-3103
MSC (2000): Primary 53C44, 58J35
Published electronically: April 30, 2009
MathSciNet review: 2506468
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Abstract: An important and natural question in the analysis of Ricci flow behavior in all dimensions $ n\geq4$ is this: What are the weakest conditions that guarantee that a solution remains smooth? In other words, what are the weakest conditions that provide control of the norm of the full Riemann curvature tensor? In this short paper, we show that the trace-free Ricci tensor is controlled in a precise fashion by the other components of the irreducible decomposition of the curvature tensor, for all compact solutions in all dimensions $ n\geq3$, without any hypotheses on the initial data.

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Additional Information

Dan Knopf
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-0257

Received by editor(s): July 14, 2008
Published electronically: April 30, 2009
Additional Notes: The author acknowledges NSF support in the form of grants DMS-0545984 and DMS-0505920.
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2009 by the author

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