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arXiv · 2005.05830

Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions

Simon Brendle·Keaton Naff
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Abstract

We extend the second part of \cite{Bre20} on the uniqueness of ancient $\kappa$-solutions to higher dimensions. In dimensions $n \geq 4$, an ancient $\kappa$-solution is a nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is $\kappa$-noncollapsed. We show that the only noncompact ancient $\kappa$-solutions up to isometry are a family of shrinking cylinders, a quotient thereof, or the Bryant soliton.

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Simon Brendle, Keaton Naff. 2020-05-12. Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions. https://doi.org/10.2140/gt.2023.27.153

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