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

Abstract

We extend the second part of \cite{Bre20} on the uniqueness of ancient $\kappa$-solutions to higher dimensions. In dimensions $n\ge 4$, 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. We show that the only noncompact ancient $\kappa$-solutions up to isometry are a family of shrinking cylinders, a quotient thereof, or the Bryant soliton.

final version, to appear G&T

References in corpus (3)

• Uniqueness of compact ancient solutions to three-dimensional Ricci flow
• Unique Asymptotics of Compact Ancient Solutions to three-dimensional Ricci flow
• Shrinking Ricci solitons with positive isotropic curvature

Cited by in corpus (7)

• Classification of bubble-sheet ovals in ${\mathbb{R}}^4$
• Ancient solutions to the Kähler Ricci flow
• Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature
• Ancient solutions to the Ricci flow with isotropic curvature conditions
• O(2)-symmetry of 3D steady gradient Ricci solitons
• Compact manifolds of dimension $n\ge 12$ with positive isotropic curvature
• Hearing the shape of ancient noncollapsed flows in ${\mathbb{R}}^4$