中文摘要：

本文通过对满足Nash不等式的黎曼流形的研究，证明了对任一完备的Ricci曲率非负的n维黎曼流形，若它满足Nash不等式，且Nash常数大于最佳Nash常数，则它微分同胚于R^n．

英文摘要：

In this paper, we study the property of Riemannian manifold satisfying Nash inequality, and prove that for any complete n-dimensional Riemannian manifold with nonnegative Ricci curvature, if the Nash inequality is satisfied and the Nash constant is more than the best Nash constant, then the manifold is diffeomorphic to R^n.