Rotational symmetry of ancient solutions to the Ricci flow in dimension $3$ -- The compact case

Abstract

In [4], we proved that every noncompact ancient $\kappa$-solution to the Ricci flow in dimension $3$ is either locally isometric to a family of shrinking cylinders, or isometric to the Bryant soliton. In the same paper, we announced that the same method implies that compact ancient $\kappa$-solutions are rotationally symmetric. In this note we provide the details of this argument.

Cited by in corpus (2)

• Unique asymptotics of ancient compact non-collapsed solutions to the 3-dimensional Ricci flow
• Equivariant $3$-manifolds with positive scalar curvature