论文标题
在有限的RICCI曲率和局部覆盖几何形状I下，Ricci-Limit空间的收敛性I
Convergence of Ricci-limit spaces under bounded Ricci curvature and local covering geometry I
论文作者
论文摘要
我们通过建立$ c^{1，α} $的规律性，将Cheeger-Gromov和Anderson的收敛定理扩展到具有有限的RICCI曲率和局部覆盖几何形状的歧管的常规极限空间，这是对这些Ricci-Limit空间可能期望的最佳规律性。作为一个应用程序，我们证明了福卡亚的纤维化定理对具有有界的RICCI曲率的折叠流形的最佳概括，这也将原始版本提高到$ c^{1，α} $限制空间。
We extend Cheeger-Gromov's and Anderson's convergence theorems to regular limit spaces of manifolds with bounded Ricci curvature and local covering geometry, by establishing the $C^{1,α}$-regularities that are the best one may expect on those Ricci-limit spaces. As an application we prove an optimal generalization of Fukaya's fibration theorem on collapsed manifolds with bounded Ricci curvature, which also improves the original version to $C^{1,α}$ limit spaces.
