On the Conditions to Extend Ricci Flow

By Bing Wang. 2007

101 citations recorded by the source corpus.

Consider {(M n , g(t)), 0 ⩽ t < T < ∞} as an unnormalized Ricci flow solution: for t ∈ [0, T). Richard Hamilton shows that if the curvature operator is uniformly bounded under the flow for all t ∈ [0, T) then the solution can be extended over T. Natasa Sesum proves that a uniform bound of Ricci tensor is enough to extend the flow. We show that if Ricci is bounded from below, then a scalar curvature integral bound is enough to extend flow, and this integral bound condition is optimal in some sense.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ef6744e6740eaf70ac9573f182d2ad25b8ba82aa

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Space of Ricci Flows I (2009, background): “In [116], the second author developed an estimate of the type |Ric| ≤ √ |Rm||R|, where √ |Rm| should be understood as the reciprocal of a regular scale.”
On the structure of almost einstein manifolds (2012, background): “Using the evolution equation of normalized scalar curvature equation (5), similar to the calculation in [42], we obtain that ∫ t2”