Geometric rigidity of quasi-isometries in horospherical products
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910108047376384 |
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| author | Ferragut, Tom |
| author_facet | Ferragut, Tom |
| contents | We prove that quasi-isometries of horospherical products of hyperbolic spaces are geometrically rigid in the sense that they are uniformly close to product maps, this is a generalisation of the result obtained by Eskin, Fisher and Whyte in [7]. Our work covers the case of solvable Lie groups of the form R ___ (N 1 x N 2), where N 1 and N 2 are nilpotent Lie groups, and where the action on R contracts the metric on N 1 while extending it on N 2. We obtain new quasi-isometric invariants and classi cations for these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04093 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometric rigidity of quasi-isometries in horospherical products Ferragut, Tom Differential Geometry Group Theory Metric Geometry We prove that quasi-isometries of horospherical products of hyperbolic spaces are geometrically rigid in the sense that they are uniformly close to product maps, this is a generalisation of the result obtained by Eskin, Fisher and Whyte in [7]. Our work covers the case of solvable Lie groups of the form R ___ (N 1 x N 2), where N 1 and N 2 are nilpotent Lie groups, and where the action on R contracts the metric on N 1 while extending it on N 2. We obtain new quasi-isometric invariants and classi cations for these spaces. |
| title | Geometric rigidity of quasi-isometries in horospherical products |
| topic | Differential Geometry Group Theory Metric Geometry |
| url | https://arxiv.org/abs/2211.04093 |