Abstract

Consider the unnormalized Ricci flow (gij)t = -2Rij for t ∈ [0, T), where T < ∞. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T), then the solution can be extended beyond T. We prove that if the Ricci curvature is uniformly bounded under the flow for all times t ∈ [0, T), then the curvature tensor has to be uniformly bounded as well.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1315-1324
Launched on MUSE
2005-12-12
Open Access
No
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