Ancient solutions to the Ricci flow in higher dimensions

Xiaolong Li; Yongjia Zhang

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arXiv · 1812.04156

Ancient solutions to the Ricci flow in higher dimensions

Xiaolong Li·Yongjia Zhang

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Abstract

In this paper, we study $\kappa$-noncollapsed ancient solutions to the Ricci flow with nonnegative curvature operator in higher dimensions. We impose one further assumption: one of the asymptotic shrinking gradient Ricci solitons is the standard cylinder $\mathbb{S}^{n-1}\times\mathbb{R}$. By making use of the properties of such ancient solutions, we generalize part one of Brendle \cite{brendle2018ancient} to higher dimensions, that is, every noncompact $\kappa$-noncollapsed rotationally symmetric ancient solution to the Ricci flow with bounded positive curvature operator must be the Bryant soliton.

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Xiaolong Li, Yongjia Zhang. 2018-12-10. Ancient solutions to the Ricci flow in higher dimensions. https://arxiv.org/abs/1812.04156

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