流形上的调和函数空间

Space of Harmonic Function on Manifolds

本文主要研究截曲率渐近非负完备的流形上的函数理论,通过证明此流形上的体积比较定理和Poincare不等式,得到了此流形上具有多项式增长的调和函数空间的维数估计.

In this paper, we mainly study the function theory on the complete manifold with asymptotically nonnegative sectional curvature. Through proving the volume comparison theorem and the Poincare inequality on this manifold, we obtain the estimates with the dimension of the space of all the polynomial growth harmonic functions on this manifold.