Cuts, flows and gradient conditions on harmonic functions
| Autor: | Gournay, Antoine |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\ell^p$. Furthermore, under a radial isoperimetric condition, groups whose isoperimetric profile is bounded by power of logarithms also have no harmonic functions with gradient in $\ell^p$. Comment: 39 pages, updated references |
| Databáze: | arXiv |
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