Uniqueness of compact ancient solutions to the higher-dimensional Ricci flow
Uniqueness of compact ancient solutions to the higher-dimensional Ricci flow
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DOI：
10.1515/crelle-2022-0075
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发表时间：
2021-02
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影响因子：
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通讯作者：
S. Brendle;P. Daskalopoulos;Keaton Naff;N. Šešum
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文献类型：
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作者：
S. Brendle;P. Daskalopoulos;Keaton Naff;N. Šešum
在n ≥ 4 {n\geq 4}维空间中，古κ解是Ricci流的非平坦的、完备的古解，它是一致PIC和弱PIC 2的，有界曲率，并且是κ-非塌陷的.本文研究了Sn {S^{n}}上n维Ricci流的古κ-解的分类，推广了[S. Brendle，P. Daskalopoulos和N. Sesum，三维Ricci流的紧致古解的唯一性，发明。Math.2262021，2，579-651]到更高维度。我们证明了这样的解决方案是等距的一个家庭的收缩圆球，或II型古代解决方案构造的佩雷尔曼。
Abstract In dimensions n ≥ 4 {n\geq 4} , an ancient κ-solution is a nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is κ-noncollapsed. In this paper, we study the classification of ancient κ-solutions to n-dimensional Ricci flow on S n {S^{n}} , extending the result in [S. Brendle, P. Daskalopoulos and N. Sesum, Uniqueness of compact ancient solutions to three-dimensional Ricci flow, Invent. Math. 226 2021, 2, 579–651] to higher dimensions. 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.