Unique Asymptotics of Compact Ancient Solutions to three-dimensional Ricci flow

Abstract

We consider compact ancient solutions to the three-dimensional Ricci flow which are noncollapsed. We prove that such a solutions is either a family of shrinking round spheres, or it has a unique asymptotic behavior as $t\to -\infty$ which we describe. This analysis applies in particular to the ancient solution constructed by Perelman.

References in corpus (1)

• Uniqueness of compact ancient solutions to three-dimensional Ricci flow

Cited by in corpus (5)

• Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions
• Ancient finite entropy flows by powers of curvature in ${\mathbb{R}}^2$
• Translating surfaces under flows by sub-affine-critical powers of Gauss curvature
• Classification of ancient flows by sub-affine-critical powers of curvature in ${\mathbb{R}}^2$
• Hearing the shape of ancient noncollapsed flows in ${\mathbb{R}}^4$