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arXiv · 1002.1061

The $p$-harmonic boundary for quasi-isometric graphs and manifolds

Michael J. Puls
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Abstract

Let $p$ be a real number greater number greater than one. Suppose that a graph $G$ of bounded degree is quasi-isometric with a Riemannian manifold $M$ with certain properties. Under these conditions we will show that the $p$-harmonic boundary of $G$ is homeomorphic to the $p$-harmonic boundary of $M$. We will also prove that there is a bijection between the $p$-harmonic functions on $G$ and the $p$-harmonic functions on $M$.

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Michael J. Puls. 2010-02-04. The $p$-harmonic boundary for quasi-isometric graphs and manifolds. https://arxiv.org/abs/1002.1061

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