具有非负Ricci曲率的开流形的基本群

The Fundamental Group of Open Manifolds with Nonnegative Ricci Curvature

我们对某些类型的Riemannian流形,通过点到极小测地圈端点的距离建立了它到极小测地圈中点的距离的一致估计,然后利用这种一致估计证明了具有非负Ricci 曲率Riemannian流形的基本群有限生成的一个定理,对著名的Milnor猜测起到更强的支持作用．

The authors improve the uniform estimates for the distance to halfway points of mininal geodesics in terms of the distance to end points on some types of Riemannian manifolds, and then prove a theorem about the finite generation of fundamental group of Riemannian manifold with nonnegative Ricci curvature which supports the famous Milnor conjecture more strongly.