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Limiting behaviour of the Ricci flow
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abstract
We will consider a {\it $\tau$-flow}, given by the equation $\frac{d}{dt}g_{ij} = -2R_{ij} + \frac{1}{\tau}g_{ij}$ on a closed manifold $M$, for all times $t\in [0,\infty)$. We will prove that if the curvature operator and the diameter of $(M,g(t))$ are uniformly bounded along the flow, then we have a sequential convergence of the flow toward the solitons.
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Cited by 1 Pith paper
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Type-I Blowup Solutions for Yang-Mills Flow
For 5 to 9 dimensions, an infinite-dimensional family of Yang-Mills flow solutions is constructed that converge, modulo gauge, to the homothetically shrinking soliton W, including asymmetric Type-I blowups.
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