高维Ricci流古解的旋转对称性

Geometry & Topology Pub Date : 2020-05-12 DOI:10.2140/gt.2023.27.153

S. Brendle, Keaton Naff

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引用次数: 15

摘要

我们将\cite{Bre18}的第二部分扩展到更高维度的古代$\kappa$ -解的唯一性。我们证明了在$n \geq 4$维数下Ricci流的每一个非紧致的、非平坦的、完整的、一致PIC和弱PIC2的古解;曲率有界;并且是$\kappa$ -非坍缩是与一组收缩的圆圆柱体(或其商)或布莱恩特孤子等距的。

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

We extend the second part of \cite{Bre18} on the uniqueness of ancient $\kappa$-solutions to higher dimensions. We show that for dimensions $n \geq 4$ every noncompact, nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is $\kappa$-noncollapsed is isometric to a family of shrinking round cylinders (or a quotient thereof) or the Bryant soliton.

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Geometry & Topology

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