Cuts, flows and gradient conditions on harmonic functions
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908557122732032 |
|---|---|
| author | Gournay, Antoine |
| author_facet | Gournay, Antoine |
| contents | 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 $\ell^p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13275 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cuts, flows and gradient conditions on harmonic functions Gournay, Antoine Group Theory Representation Theory 31C05, 22D10, 20J06, 43A15, 05C81, 20F69 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 $\ell^p$. |
| title | Cuts, flows and gradient conditions on harmonic functions |
| topic | Group Theory Representation Theory 31C05, 22D10, 20J06, 43A15, 05C81, 20F69 |
| url | https://arxiv.org/abs/2206.13275 |