递归图和（强）可分解图
Recurrent and (strongly) resolvable graphs
摘要：
我们发展了一种新的方法来研究无穷权图上的常返性和非常数调和函数的存在性。该方法基于度量边界子集相对于内在度量的能力。主要工具是在这样的边界和路径的空集合中的极集合之间的连接。这种联系依赖于有限能量的适当发散函数。
英文摘要：
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool is a connection between polar sets in such boundaries and null sets of paths. This connection relies on suitably diverging functions of finite energy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
