The p-harmonic boundary and Dₚ-massive subsets of a graph of bounded degree

الأصل · EN

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 Dₚ-massive subsets of Γ. In particular, if there are n pairwise disjoint Dₚ-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.