Geometric rigidity of quasi-isometries in horospherical products

Rigidité géométrique des quasi-isométries des produits horosphériques.

Tom Ferragut (1)

1 UM - Université de Montpellier

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 × 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.

Domaines: Théorie des groupes [math.GR]; Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Tom Ferragut. Geometric rigidity of quasi-isometries in horospherical products. 2022. ⟨hal-03843098v1⟩