论文标题
关于未负RICCI曲率的开放式歧管中的大地环的逃脱速率
On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature
论文作者
论文摘要
A consequence of the Cheeger-Gromoll splitting theorem states that for any open manifold $(M,x)$ of nonnegative Ricci curvature, if all the minimal geodesic loops at $x$ that represent elements of $π_1(M,x)$ are contained in a bounded ball, then $π_1(M,x)$ is virtually abelian.我们概括了上述结果：如果这些最小代表$π_1（m，x）$的测量循环从任何有限的度量球中逃脱，以sublinear速率相对于其长度，则$π_1（m，x）$几乎是Abelian。
A consequence of the Cheeger-Gromoll splitting theorem states that for any open manifold $(M,x)$ of nonnegative Ricci curvature, if all the minimal geodesic loops at $x$ that represent elements of $π_1(M,x)$ are contained in a bounded ball, then $π_1(M,x)$ is virtually abelian. We generalize the above result: if these minimal representing geodesic loops of $π_1(M,x)$ escape from any bounded metric balls at a sublinear rate with respect to their lengths, then $π_1(M,x)$ is virtually abelian.
