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Ancient solutions to the Ricci flow in higher dimensions by Li, Xiaolong; Zhang, Yongjia is a scholarly article available to read on EtoBox.

What is Ancient solutions to the Ricci flow in higher dimensions about?

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.

Author

Li, Xiaolong; Zhang, Yongjia

Published

2018

Language

EN