Geometric rigidity of quasi-isometries in horospherical products
Abstract
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 Ë .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.
Fields of Study & Subjects
Analytic and geometric function theory
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 3
- Pages
- 863–954
- Publication date
- 1 April 2026
- Language
- EN