Mathematics > Differential Geometry
[Submitted on 10 Dec 2018 (v1), last revised 14 May 2020 (this version, v2)]
Title:Ancient solutions to the Ricci flow in higher dimensions
View PDFAbstract: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.
Submission history
From: Xiaolong Li [view email][v1] Mon, 10 Dec 2018 23:49:04 UTC (22 KB)
[v2] Thu, 14 May 2020 07:16:01 UTC (24 KB)
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