Liouville properties of harmonic maps (Q1910667)

The author gives careful contexts and proofs of several theorems asserting that a harmonic map \(u : M \to N\) between complete Riemannian manifolds must be constant. For instance: \(M\) is quasi-isometric to a noncompact manifold with Ricci curvature \(\geq 0\); \(N\) simply connected with Riemannian sectional curvature \(\leq 0\); and \(u(M)\) suitably small.