Some results concerning the p-Royden and p-harmonic boundaries of a graph of bounded degree

2010/12/11 by Puls, Michael
#31C45 #43A15 #60J50 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1012.2473

Abstract

Let p be a real number greater than one and let Γ be a connected graph of bounded degree. We show that the p-Royden boundary of Γ with the p-harmonic boundary removed is a F_σ-set. We also characterize the p-harmonic boundary of Γ in terms of the intersection of the extreme points of a certain subset of one-sided infinite paths in Γ.

Related

• Graphs of bounded degree and the p-harmonic boundary
• The p-harmonic boundary and D_p-massive subsets of a graph of bounded degree
• The p-harmonic boundary for quasi-isometric graphs and manifolds
• The p-Royden and p-harmonic boundaries for metric measure spaces
• The Boundary of a Graph and its Isoperimetric Inequality