Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions

Abstract

We extend the second part of \cite{Bre18} on the uniqueness of ancient $\kappa$-solutions to higher dimensions. We show that for dimensions $n \geq 4$ every noncompact, nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is $\kappa$-noncollapsed is isometric to a family of shrinking round cylinders (or a quotient thereof) or the Bryant soliton.