任何具有Liouville性质的可平面图都是顺从的
Every planar graph with the Liouville property is amenable
摘要：
我们引入了一个加强的概念的瞬态平面映射，以放松的标准条件的有界度出现在各种结果，特别是，存在的Dirichlet调和函数证明Benjamini和Schramm。作为推论，我们得到了每个平面非顺从图都存在Dirichlet调和函数.
英文摘要：
We introduce a strengthening of the notion of transience for planar maps in order to relax the standard condition of bounded degree appearing in various results, in particular, the existence of Dirichlet harmonic functions proved by Benjamini and Schramm. As a corollary we obtain that every planar non-amenable graph admits Dirichlet harmonic functions.
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。
