中文摘要：

本文主要研究了在曲率渐近非负流形上的一些性质，其上不存在非常数的正调和函数；若其调和函数是对一固定指数d的多项式增长，那么由这些调和函数所组成的空间的维数≤Cd^CD，而且此流形的体积为无穷大等．

英文摘要：

In this paper, the author proves some results on the manifold with asymptotically nonnegative curvature： there is no nontrivially positive harmonic function; the dimension of the space of harmonic functions with polynomial growth of a fixed rate d ≤ Cd^CD; and the volumn of this manifold is infinite.