中文摘要：

通过对Poisson方程解的估计，证明了对任一完备非紧Ricci曲率非负的黎曼流形，若它的数量曲率的平均值满足一定的衰竭条件，则它是Ricci平坦的．

英文摘要：

The solution of the Poisson equation is estimated, and it is proved that for any complete noncompact Riemannian manifold with nonnegative Ricci curvature, if the mean value of the scalar curvature satisfies a certain decaying condition, it is Ricci flat.