We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. We consider the behavior of Ricci flow with surgery starting from a fixed initial compact Riemannian 3-manifold, as the surgery parameter varies. We prove that the flow with surgery subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows.

中文翻译：

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奇异 Ricci 流 I

我们引入了奇异 Ricci 流，它们是受某些渐近条件约束的 Ricci 流时空。随着手术参数的变化，我们考虑了从固定的初始紧凑黎曼 3 流形开始的手术中 Ricci 流的行为。我们证明，当手术参数趋于零时，手术流会收敛到奇异 Ricci 流。我们建立了奇异 Ricci 流的许多几何和分析性质。