AI 中文总结
本研究证明从奇异Reifenberg空间出发、满足尺度不变曲率界等条件的Ricci流唯一性，并据此在极限空间上规范定义光滑结构，推广了Perelman稳定性定理。
AI 中文摘要
我们考虑从奇异初始数据出发的 Ricci 流的唯一性问题。即使初始数据是光滑且光滑地获得的，在完全非紧情形下，唯一性也并非在完全一般性下已知。当从非光滑初始数据出发时，即使在紧致情形下，已知结果也非常少。我们获得了具有尺度不变曲率界、适当的非坍缩假设以及截面曲率下界的 Ricci 流的唯一性结果，这些流从（可能奇异的）Reifenberg 空间出发。作为我们结果以及 Simon–Topping 和 Lai 所获存在性结果的推论，存在一种规范方式在任何 Reifenberg 一致体积非坍缩 PIC2 极限空间上定义光滑结构。进一步，我们获得了这些极限空间的 Perelman 稳定性定理的微分同胚版本。
英文摘要
We consider the problem of uniqueness of Ricci flows, starting from singular initial data. Even when the initial data is smooth and smoothly obtained, in the complete noncompact case uniqueness is not known in full generality. When starting from nonsmooth initial data, very little is known, even in the compact case. We obtain a uniqueness result for Ricci flows with scaling-invariant curvature bounds, a suitable noncollapsing assumption, and sectional curvature lower bounds, coming out of (possibly singular) Reifenberg spaces. As a consequence of our result, and existence results obtained by Simon--Topping and Lai, there is a canonical way to define a smooth structure on any Reifenberg uniformly volume-noncollapsed PIC2 limit space. Further, we obtain a diffeomorphic version of Perelman's stability theorem for these limit spaces.
