Journal
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume 2023, Issue 795, Pages 85-138Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/crelle-2022-0075
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This paper studies the classification of ancient kappa-solutions to n-dimensional Ricci flow on Sn, extending the previous results in three dimensions. The study shows that such solutions are either isometric to a family of shrinking round spheres, or the Type II ancient solution constructed by Perelman.
In dimensions n >= 4, an ancient kappa-solution is a nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is kappa-noncollapsed. In this paper, we study the classification of ancient kappa-solutions to n-dimensional Ricci flow on Sn, 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), no. 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.
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