Ancient solutions to the Ricci flow in dimension 3

Abstract

It is known from work of Perelman that any finite-time singularity of the Ricci flow on a compact three-manifold is modeled on an ancient $\kappa$-solution. We prove that the every noncompact ancient $\kappa$-solution in dimension $3$ is isometric to either the shrinking cylinders (or a quotient thereof), or the Bryant soliton.

revised version, to appear in Acta Mathematica

References in corpus (1)

• Uniqueness of convex ancient solutions to mean curvature flow in ${\mathbb{R}}^3$

Cited by in corpus (10)

• Curvature growth of some 4-dimensional gradient Ricci soliton singularity models
• Unique Asymptotics of Compact Ancient Solutions to three-dimensional Ricci flow
• Rotational symmetry of ancient solutions to the Ricci flow in dimension $3$ -- The compact case
• A family of 3d steady gradient solitons that are flying wings
• Producing 3d Ricci flows with non-negative Ricci curvature via singular Ricci flows
• Rotationally symmetric Ricci flow on ${\mathbb{R}}^{n+1}$
• Ancient solutions to the Kähler Ricci flow
• Ancient finite entropy flows by powers of curvature in ${\mathbb{R}}^2$
• Ancient solutions to the Ricci flow with isotropic curvature conditions
• Asymptotic curvature estimate for steady solitons