Rigidity of convex co-compact diagonal actions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910558917230592 |
|---|---|
| author | Dey, Subhadip Liu, Beibei |
| author_facet | Dey, Subhadip Liu, Beibei |
| contents | Kleiner-Leeb and Quint showed that convex subsets in higher-rank symmetric spaces are very rigid compared to rank 1 symmetric spaces. Motivated by this, we consider convex subsets in products of proper CAT(0) spaces $X_1\times X_2$ and show that for any two convex co-compact actions $ρ_i(Γ)$ on $X_i$, where $i=1, 2$, if the diagonal action of $Γ$ on $X_1\times X_2$ via $ρ=(ρ_1, ρ_2)$ is also convex co-compact, then under a suitable condition, $ρ_1(Γ)$ and $ρ_2(Γ)$ have the same marked length spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of convex co-compact diagonal actions Dey, Subhadip Liu, Beibei Geometric Topology Group Theory Metric Geometry 51F30, 20F67, 20F65, 53C24 Kleiner-Leeb and Quint showed that convex subsets in higher-rank symmetric spaces are very rigid compared to rank 1 symmetric spaces. Motivated by this, we consider convex subsets in products of proper CAT(0) spaces $X_1\times X_2$ and show that for any two convex co-compact actions $ρ_i(Γ)$ on $X_i$, where $i=1, 2$, if the diagonal action of $Γ$ on $X_1\times X_2$ via $ρ=(ρ_1, ρ_2)$ is also convex co-compact, then under a suitable condition, $ρ_1(Γ)$ and $ρ_2(Γ)$ have the same marked length spectrum. |
| title | Rigidity of convex co-compact diagonal actions |
| topic | Geometric Topology Group Theory Metric Geometry 51F30, 20F67, 20F65, 53C24 |
| url | https://arxiv.org/abs/2408.03462 |