Superrigidity, generalized harmonic maps and uniformly convex spaces

2006/06/11 by Tsachik Gelander, Anders Karlsson, Gelander, T. +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0606256

openalex publication_date 2006/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove several superrigidity results for isometric actions on metric spaces satisfying some convexity properties. First, we extend some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of locally compact groups. Second, we include the proof of an unpublished result on commensurability superrigidity due to Margulis. The proofs rely on certain notions of harmonic maps and the study of their existence, uniqueness, and continuity.

Cited by

• Cocycle superrigidity for median spaces of finite rank

Related

• Harmonic Maps into Euclidean Buildings and Non-Archimedean Superrigidity
• Invariant strictly convex renormings
• Actions of higher rank groups on uniformly convex Banach spaces
• On fixed points and uniformly convex spaces
• Remarks on quasi-isometric non-embeddability into uniformly convex Banach spaces