Ancient solutions to the Ricci flow with isotropic curvature conditions

Abstract

We show that every $n$-dimensional, $\kappa$-noncollapsed, noncompact, complete ancient solution to the Ricci flow with uniformly PIC for $n=4$ or $n\ge 12$ has weakly PIC${}_2$ and bounded curvature. Combining this with earlier results, we prove that any such solution is isometric to either a family of shrinking cylinders (or a quotient thereof) or the Bryant soliton. Also, we classify all complex 2-dimensional, $\kappa$-noncollapsed, complete ancient solutions to the Kähler Ricci flow with weakly PIC.

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci Flow and the Poincare Conjecture
• Shrinking Ricci solitons with positive isotropic curvature