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We define a tamed condition on Kahler Ricci flow on Fano manifolds. If the flow satisfies the tamed condition, then the convergence of the flow can be calculated from the initial algebraic geometry condition. In dimension 2, we use weak-compactness argument to show that the tamed condition always holds. Therefore, the convergence of the Kahler Ricci flow is determined by the initial algebraic condition. This method can be applied to the Kahler Ricci flow on Fano orbifold surface to obtain some new KE metrics. |
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