We consider solutions $(M, g(t)), 0 \leq t \lt T$, to Ricci flow on compact, connected four dimensional manifolds without boundary. We assume that the scalar curvature is bounded uniformly, and that $T \lt \infty$. In this case, we show that the metric space $(M, d(t))$ associated to $(M, g(t))$ converges uniformly in the $C^0$ sense to $(X, d)$, as $t \nearrow T$, where $(X, d)$ is a $C^0$ Riemannian orbifold with at most finitely many orbifold points. Estimates on the rate of convergence near and away from the orbifold points are given. We also show that it is possible to continue the flow past $(X, d)$ using the orbifold Ricci flow.

中文翻译：

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扩展具有标量曲率的四维Ricci流

我们考虑解$（M，g（t）），0 \ leq t \ lt T $，在无边界的紧凑，连通的四维流形上的Ricci流。我们假设标量曲率是均匀有界的，并且$ T \ lt \ infty $。在这种情况下，我们表明与$（M，g（t））$关联的度量空间$（M，d（t））$在$ C ^ 0 $的意义上均匀收敛于$（X，d）$ ，如$ t \ nearrow T $，其中$（X，d）$是一个CC = 0 $ Riemannian单倍数，最多具有有限的多个单倍点。给出了在圆点附近和远离圆点的收敛速度的估计。我们还表明，可以使用折线Ricci流继续经过$（X，d）$ 。