The \(p\)-harmonic boundary and \(D_p\)-massive subsets of a graph of bounded degree

Authors

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

Keywords:

\(p\)-harmonic boundary, \(D_p\) 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 \(\Gamma\) be a graph of bounded degree. We investigate links between the \(p\)-harmonic boundary of \(\Gamma\)and the \(D_p\)-massive subsets of \(\Gamma\). In particular, if there are \(n\) pairwise disjoint \(D_p\)-massive subsets of \(\Gamma\), then the \(p\)-harmonic boundary of \(\Gamma\) 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

Vol. 89 No. 1 (2014)

Section

Articles
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