The Martin boundary of an extension by a hyperbolic group
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866917622936764416 |
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| author | Bispo, Sara Ruth Pires Stadlbauer, Manuel |
| author_facet | Bispo, Sara Ruth Pires Stadlbauer, Manuel |
| contents | We prove uniform Ancona-Gouëzel-Lalley inequalities for an extension by a hyperbolic group $G$ of a Markov map which allows to deduce that the visual boundary of the group and the Martin boundary are Hölder equivalent. As application, we identify the set of minimal conformal measures of a regular cover of a convex-cocompact CAT(-1)-manifold with the visual boundary of the covering group, provided that this group is hyperbolic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_03723 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Martin boundary of an extension by a hyperbolic group Bispo, Sara Ruth Pires Stadlbauer, Manuel Dynamical Systems 37A50, 37C30, 20F69 We prove uniform Ancona-Gouëzel-Lalley inequalities for an extension by a hyperbolic group $G$ of a Markov map which allows to deduce that the visual boundary of the group and the Martin boundary are Hölder equivalent. As application, we identify the set of minimal conformal measures of a regular cover of a convex-cocompact CAT(-1)-manifold with the visual boundary of the covering group, provided that this group is hyperbolic. |
| title | The Martin boundary of an extension by a hyperbolic group |
| topic | Dynamical Systems 37A50, 37C30, 20F69 |
| url | https://arxiv.org/abs/2005.03723 |