In this paper, we study the classification of \(\kappa \)-noncollapsed ancient solutions to three-dimensional Ricci flow on \(S^3\). We prove that such a solution is either isometric to a family of shrinking round spheres, or the Type II ancient solution constructed by Perelman.

中文翻译：

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三维 Ricci 流的紧凑古解的唯一性

在本文中，我们研究了\(\kappa \)对\(S^3\)上三维 Ricci 流的非塌陷古解的分类。我们证明这样的解决方案要么与一系列缩小的圆形球体等距，要么与 Perelman 构建的 Type II 古代解决方案等距。