We will consider a tau-flow, given by the equation d/dt g(ij) = -2R(ij) + 1/tau g(ij) on a closed manifold M, for all times t is an element of [0, infinity). 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. If we also assume that one of the limit solitons is integrable, then we have a convergence toward a unique soliton, up to a diffeomorphism.
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机译：我们将考虑在闭合歧管M上由方程d / dt g（ij）= -2R（ij）+ 1 / tau g（ij）给出的tau流量，对于所有时间t都是[0，无限）。我们将证明，如果曲率算子和（M，g（t））的直径沿流均匀地有界，则流向孤子的流动将有顺序收敛。如果我们还假设极限孤子之一是可积的，则我们趋向于一个唯一的孤子，直至微分同构。
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