Harmonic maps of infinite energy and rigidity results for quasiprojective varieties (Q1897734)

In this paper, certain harmonic maps into locally Hermitian symmetric spaces of noncompact type and finite volume are described. These maps may have infinite energy, but they are nevertheless amenable to Bochner type identities since the growth of the energy density near infinity is sufficiently well controlled. With the help of these maps, the geometric superrigidity results of Jost-Yau in the noncompact case are completed. Extensions to representations of fundamental groups of algebraic varieties are also described. The paper is a research announcement. Details will appear elsewhere.