论文标题
在谐波功能上的切割，流量和梯度条件
Cuts, flows and gradient conditions on harmonic functions
论文作者
论文摘要
降低的同种学促使人们查看满足某些梯度条件的谐波功能。如果$ g $是两个无限组的直接产品或一个（fc-central）划分的群体，则在其cayley图中没有梯度的谐波功能。从中，Metabelian $ g $在$ \ ell^p $中没有谐波功能。此外，在径向等级条件下，等级轮廓的组受对数功率的界限也没有谐波功能，梯度在$ \ ell^p $中。
Reduced cohomology motivates to look at harmonic functions which satisfy certain gradient conditions. If $G$ is a direct product of two infinite groups or a (FC-central)-by-cyclic group, then there are no harmonic functions with gradient in $c_0$ on its Cayley graphs. From this, it follows that a metabelian group $G$ has no harmonic functions with gradient in $\ell^p$. Furthermore, under a radial isoperimetric condition, groups whose isoperimetric profile is bounded by power of logarithms also have no harmonic functions with gradient in $\ell^p$.
