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

Authors

  • M. J. Puls John Jay College (CUNY)

Keywords:

p-harmonic boundary, Dp massive set, p-harmonic function, asymptotically constant functions, extreme points of a path

Abstract

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 Γand 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. 10.1017/S0004972713000439

Published

2013-12-02

Issue

Section

Articles