Affiliation:
1. Department of Mathematics , Columbia University , 2990 Broadway , New York City , NY 10027 , USA
2. Department of Mathematics , Rutgers University , Felinghuysen Rd , Pitscataway , NJ 08854 , USA
Abstract
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.
Subject
Applied Mathematics,General Mathematics
Cited by
3 articles.
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