Geometric rigidity of quasi-isometries in horospherical products

Geometric rigidity of quasi-isometries in horospherical products TOM FERRAGUTWe 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 a result obtained by Eskin, Fisher and Whyte (2012).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 classifications for these spaces.