Median geometry for spaces with measured walls and for groups

Journal article

We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of compatibility possible with median geometry. The result follows from an analysis of a quasification of median geometry that provides a geometric characterization of spaces at a finite Hausdorff distance from a median space. The case of complex hyperbolic metric spaces is different; we show that these spaces cannot be at finite Hausdorff distance from a median space.

Authors: Chatterji, I; Druţu, C

• Alternative title: Median geometry for spaces with measured walls..
• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Mathematische Annalen
• Volume: 393
• Issue: 3-4
• Pages: 2925-2952
• Publication date: 2025-10-25
• Acceptance date: 2025-09-10
• DOI: 10.1007/s00208-025-03289-1
• EISSN: 1432-1807
• ISSN: 0025-5831
• Language: English
• Keywords: 22F50; Primary 20F65; Secondary 46B04; 20F67