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arXiv · 1402.3126

Absence of non-constant harmonic functions with $\ell^p$-gradient in some semi-direct products

Antoine Gournay
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Abstract

To obtain groups with bounded harmonic functions (which are not hyperbolic), one of the most frequent way is to look at some semi-direct products (\eg lamplighter groups). The aim here is to show that many of these semi-direct products do not admit harmonic functions with gradient in $\ell^p$, for $p\in [1,\infty[$.

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Antoine Gournay. 2014-02-13. Absence of non-constant harmonic functions with $\ell^p$-gradient in some semi-direct products. https://arxiv.org/abs/1402.3126

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