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arXiv · 1012.2473

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

Michael Puls
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Abstract

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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Michael Puls. 2010-12-11. Some results concerning the $p$-Royden and $p$-harmonic boundaries of a graph of bounded degree. https://arxiv.org/abs/1012.2473

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