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arXiv · 1108.4381

The $p$-harmonic boundary and $D_p$-massive subsets 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 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.

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Michael Puls. 2011-08-22. The $p$-harmonic boundary and $D_p$-massive subsets of a graph of bounded degree. https://arxiv.org/abs/1108.4381

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