Estimating the trace-free Ricci tensor in Ricci flow

Knopf, Dan

doi:10.1090/S0002-9939-09-09940-7

Estimating the trace-free Ricci tensor in Ricci flow
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by Dan Knopf

Proc. Amer. Math. Soc. 137 (2009), 3099-3103

DOI: https://doi.org/10.1090/S0002-9939-09-09940-7

Published electronically: April 30, 2009

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Abstract:

An important and natural question in the analysis of Ricci flow behavior in all dimensions $n\geq 4$ 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 $n\geq 3$, without any hypotheses on the initial data.

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