一类完备Riemann流形上的有界调和函数

Bounded Harmonic Functions on a Class of Complete Riemannian Manifolds

本文我们将对一类完备Ｒｉｅｍａｎｎ流形上的有界调和函数所组成的线性空间的维数的上界进行估计，同时给出了一个关于测地球体积的Ｂｉｓｈｏｐ－Ｇｒｏｍｏｖ型体积比较定理。

In this paper,we consider the dimension of the space of bounded harmonic functionson a class of Riemannian manifolds. An upper bound of the dimension is obtained. In themeanwhile, a volume comparison theorem of Bishop-Gromov type on the geodesic balls is alsogiven on such kinds of manifolds