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arXiv · 2005.11866

Ancient solutions to the Ricci flow with isotropic curvature conditions

Jae Ho Cho·Yu Li
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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 K\"ahler Ricci flow with weakly PIC.

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Jae Ho Cho, Yu Li. 2020-05-25. Ancient solutions to the Ricci flow with isotropic curvature conditions. https://arxiv.org/abs/2005.11866

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