论文标题
较高维度的RICCI流的古代解决方案的旋转对称性
Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions
论文作者
论文摘要
我们将\ cite {bre20}的第二部分扩展到了古代$κ$ solutions的独特性到更高尺寸的独特性。在尺寸中，$ n \ geq 4 $，一种古老的$κ$ - 解决方案是一种非flat，完整的，古老的ricci流动解决方案，是均匀的图片和弱pic2的；有弯曲的曲率；并且是$κ$ -Noncollaps。我们表明，等轴测图上唯一的非巨大$κ$ solutions是一个缩小的圆柱体，其商的家族，或者是布莱恩特·索利顿（Bryant Soliton）。
We extend the second part of \cite{Bre20} on the uniqueness of ancient $κ$-solutions to higher dimensions. In dimensions $n \geq 4$, an ancient $κ$-solution is a nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2; has bounded curvature; and is $κ$-noncollapsed. We show that the only noncompact ancient $κ$-solutions up to isometry are a family of shrinking cylinders, a quotient thereof, or the Bryant soliton.
