Harmonic maps of infinite energy and rigidity results for representations of fundamental groups of quasiprojective varieties (Q1392739)

The paper shows the existence of harmonic maps associated with reductive homomorphisms of the fundamental group of a quasiprojective variety into a linear algebraic group over an Archimedean or \(p\)-adic field. The constructed map may have infinite energy, but it satisfies suitable estimates at infinity, and it is pluriharmonic. This map is used to complete a previous result of Jost-Yau on strong rigidity of nonuniform lattices in Hermitian symmetric spaces, and to drop a certain topological restriction in the theory of representations of fundamental groups of quasiprojective varieties, previously developed by the authors.