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THE $p$-HARMONIC BOUNDARY AND ${D}_{p} $-MASSIVE SUBSETS OF A GRAPH OF BOUNDED DEGREE
Published online by Cambridge University Press: 12 June 2013
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 show that the converse of this statement is also true.
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- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 89 , Issue 1 , February 2014 , pp. 149 - 158
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.