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Uniqueness of compact ancient solutions to the higher-dimensional Ricci flow.
- Source :
- Journal für die Reine und Angewandte Mathematik; Feb2023, Vol. 2023 Issue 795, p85-138, 54p
- Publication Year :
- 2023
-
Abstract
- In dimensions n ≥ 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 , 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- THREE-dimensional flow
RICCI flow
CURVATURE
Subjects
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2023
- Issue :
- 795
- Database :
- Complementary Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 161627306
- Full Text :
- https://doi.org/10.1515/crelle-2022-0075