Abstract
In this paper, we study the behavior of harmonic maps into complexes with branching differentiable manifold structure. The main examples of such target spaces are Euclidean and hyperbolic buildings. We show that a harmonic map from an irreducible symmetric space of noncompact type other than real or complex hyperbolic into these complexes are non-branching. As an application, we prove rank-one and higher-rank superrigidity for the isometry groups of a class of complexes which includes hyperbolic buildings as a special case.
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Daskalopoulos, G., Mese, C. & Vdovina, A. Superrigidity of Hyperbolic Buildings. Geom. Funct. Anal. 21, 905–919 (2011). https://doi.org/10.1007/s00039-011-0124-9
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DOI: https://doi.org/10.1007/s00039-011-0124-9