论文标题
含有赤道的Riemannian歧管的刚度
Rigidity of riemannian manifolds containing an equator
论文作者
论文摘要
在本文中，我们证明了一个Riemannian $ n $ manifold $ m $，上面的截面曲率为$ 1 $，其中包含最小的$ 2 $ 2 $ - 面积$4π$，该$4π$至少具有$ n-2 $的指数$ n-2 $具有恒定的截面曲率$ 1 $。证明使用了从最小的亚策略中流出的古代平均曲率流的构造。结果，我们还证明了Simon-Smith最小球体的刚性结果。
In this paper, we prove that a Riemannian $n$-manifold $M$ with sectional curvature bounded above by $1$ that contains a minimal $2$-sphere of area $4π$ which has index at least $n-2$ has constant sectional curvature $1$. The proof uses the construction of ancient mean curvature flows that flow out of a minimal submanifold. As a consequence we also prove a rigidity result for the Simon-Smith minimal spheres.
