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arXiv · 2206.13275

Cuts, flows and gradient conditions on harmonic functions

Antoine Gournay
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Abstract

Reduced cohomology motivates to look at harmonic functions which satisfy certain gradient conditions. If $G$ is a direct product of two infinite groups or a (FC-central)-by-cyclic group, then there are no harmonic functions with gradient in $c_0$ on its Cayley graphs. From this, it follows that a metabelian group $G$ has no harmonic functions with gradient in $\ell^p$.

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Antoine Gournay. 2022-06-27. Cuts, flows and gradient conditions on harmonic functions. https://arxiv.org/abs/2206.13275

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