Abstract.
We prove several superrigidity results for isometric actions on Busemann non-positively curved uniformly convex metric spaces. In particular we generalize some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of locally compact groups, and we give a proof of an unpublished result on commensurability superrigidity due to G.A. Margulis. The proofs rely on certain notions of harmonic maps and the study of their existence, uniqueness, and continuity.
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T.G. partially supported by NSF grant DMS-0404557. A.K. partially supported by VR grant 2002-4771. G.A.M. partially supported by NSF grant DMS-0244406. T.G. and G.A.M. partially supported by BSF grant 2004010.
Submitted: June 2006, Revision: June 2007, Accepted: July 2007
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Gelander, T., Karlsson, A. & Margulis, G.A. Superrigidity, Generalized Harmonic Maps and Uniformly Convex Spaces. GAFA Geom. funct. anal. 17, 1524–1550 (2008). https://doi.org/10.1007/s00039-007-0639-2
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DOI: https://doi.org/10.1007/s00039-007-0639-2