Consider the unnormalized Ricci flow (8 ij)t = -2R ij 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.
|Original language||English (US)|
|Number of pages||10|
|Journal||American Journal of Mathematics|
|State||Published - Dec 1 2005|
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