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

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

2010-12-11

arxiv.org/abs/1012.2473v2

Mathematics

Functional Analysis

Fixed minor typos. No other changes to paper

Scientific paper

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

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