论文标题
非负RICCI曲率，度量锥和虚拟Abelianness
Nonnegative Ricci curvature, metric cones, and virtual abelianness
论文作者
论文摘要
令$ m $为具有非负RICCI曲率的开放$ n $ manifold。我们证明，如果它的逃逸率不是$ 1/2 $，并且其Riemannian Universal Cover是无穷大的Conic，也就是说，Universal Cover的每个渐近锥$（y，y）$是一个公制的圆锥，则具有顶点$ y $，然后是$π_1（m）$，包含一个亚洲的有限指数亚级。此外，如果通用覆盖物具有至少$ l $的欧几里得量增长，则我们可以通过固定的$ c（n，l）$进一步绑定该指数。
Let $M$ be an open $n$-manifold with nonnegative Ricci curvature. We prove that if its escape rate is not $1/2$ and its Riemannian universal cover is conic at infinity, that is, every asymptotic cone $(Y,y)$ of the universal cover is a metric cone with vertex $y$, then $π_1(M)$ contains an abelian subgroup of finite index. If in addition the universal cover has Euclidean volume growth of constant at least $L$, we can further bound the index by a constant $C(n,L)$.
