在本文中，我们主要研究具有非负曲率完备非紧流形的体积增长与闭测地线及距离函数临界点一些关系。

The paper gives a simple version and progress of the open Riemannian manifolds with nonnegative Ricci curvature and large volume growth from 1990.

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并由此讨论了紧致的非单连通黎曼流形上无穷多的闭测地线存在性问题。

Also, the paper discuss the existence of the infinite closed geodesics of a compact no-simply connected Riemannian manifold.

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讨论了紧致非单连通的具非负曲率的流形的一些几何性质，并应用它们证明了具非负曲率的紧致非单连通曲面必为平坦的。

With the help of them, it can be proved that the non-simply connected compact surface with nonnegative curvature must be flat.

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