Uniqueness of compact ancient solutions to the higher dimensional Ricci flow

Abstract

In this paper, we study the classification of $\kappa$-noncollapsed ancient solutions to n-dimensional Ricci flow on $S^n$, extending the result in [13] 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.

arXiv admin note: substantial text overlap with arXiv:2002.12240