Representations of Discrete Groups and Geometric Topology on Manifoldss, Josai University

We show that every one-harmonic map, in the sense of Trapani and Valli, from a Hadamard surface of pinched negative curvature to H2 has image equal to the interior of the convex hull of a subset of ∂∞ H2. The proof relies on Minkowski geometry, by interpreting one-harmonic maps as the Gauss maps of convex surfaces