论文标题
liouville定理在Ricci收缩术中具有恒定标态曲率及其应用
Liouville Theorem on Ricci shrinkers with constant scalar curvature and its application
论文作者
论文摘要
在本文中，我们考虑了具有恒定标态曲率的Ricci孤子的梯度上的谐波功能。在不使用梯度估计的情况下，证明了一个liouville定理：在梯度缩小的ricci孤子子具有恒定标态曲率的梯度上，任何有限的谐波函数都是恒定的。作为应用程序，我们表明谐波函数具有多项式生长的空间具有有限的维度。
In this paper we consider harmonic functions on gradient shrinking Ricci solitons with constant scalar curvature. A Liouville theorem is proved without using gradient estimate : any bounded harmonic function is constant on gradient shrinking Ricci solitons with constant scalar curvature. As an application, we show that the space of harmonic functions with polynomial growth has finite dimension.
