The Geometry of (p,q)-Harmonic Maps

This paper studies (p,q)-harmonic maps by unified geometric analytic methods. First, we deduce variation formulas of the (p,q)-energy functional. Second, we analyze weakly conformal and horizontally conformal (p,q)-harmonic maps and prove Liouville results for (p,q)-harmonic maps under Hessian and asymptotic conditions on complete Riemannian manifolds. Finally, we define the (p,q)-SSU manifold and prove that non-constant stable (p,q)-harmonic maps do not exist.