The $p$-harmonic boundary and $D_p$-massive subsets of a graph of bounded degree
Michael J. Puls · arXiv (Cornell University) · 2011
Let $p$ be a real number greater than one and let $Γ$ be a graph of bounded degree. We investigate links between the $p$-harmonic boundary of $Γ$ and the $D_p$-massive subsets of $Γ$. In particular, if there are $n$ pairwise disjoint $D_p$-massive subsets of $Γ$, then the $p$-harmonic boundary of $Γ$ consists of at least $n$ elements. We also show that the converse of this statement is also true.