Positive harmonic functions on groups and covering spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909219897212928 |
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| author | Polymerakis, Panagiotis |
| author_facet | Polymerakis, Panagiotis |
| contents | We show that if $p \colon M \to N$ is a normal Riemannian covering, with $N$ closed, and $M$ has exponential volume growth, then there are non-constant, positive harmonic functions on $M$. This was conjectured by Lyons and Sullivan in \cite{LS}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_11723 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Positive harmonic functions on groups and covering spaces Polymerakis, Panagiotis Differential Geometry Probability We show that if $p \colon M \to N$ is a normal Riemannian covering, with $N$ closed, and $M$ has exponential volume growth, then there are non-constant, positive harmonic functions on $M$. This was conjectured by Lyons and Sullivan in \cite{LS}. |
| title | Positive harmonic functions on groups and covering spaces |
| topic | Differential Geometry Probability |
| url | https://arxiv.org/abs/1906.11723 |