论文标题
Ricci收缩剂的本地差距定理
A local gap theorem for Ricci shrinkers
论文作者
论文摘要
我们证明了RICCI收缩剂的本地差距定理，该定理指出，如果以最小功能的最小功能的大球上的本地$ $ $ $ $ $ $ $ $ 1 $ $ 1 $接近$ 0 $，则收缩器必须是Flat Gaussian收缩器。关于我们的结果，横田[YO09，YO12]证明了同样的结果，假设全球$μ$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $。我们的结果表明，收缩器的局部几何形状如何控制全局几何形状，这也在[LW19，LW20，LW21]中进行了讨论。
We prove a local gap theorem for Ricci shrinkers, which states that if the local $μ$-functional at scale $1$ on a large ball centered at the minimum point of the potential function is close enough to $0$, then the shrinker must be the flat gaussian shrinker. In relation to our result, Yokota [Yo09,Yo12] proved the same result assuming the global $μ$-functional to be close enough to $0$. Our result shows an aspect of how the local geometry of a shrinker controls the global geometry, which is also discussed in [LW19,LW20,LW21].
