Convergence of the Ricci flow toward a unique soliton

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We will consider a τ-flow, given by the equation d/dtgij = -2Rij + 1τgij on a closed manifold M, for all times t∈ [0,∞). We will prove that if the curvature operator and the diameter of (M,g(t)) are uniformly bounded along the flow and if one of the limit solitons is integrable, then we have a convergence of the flow toward a unique soliton, up to a diffeomorphism.