Journal of the
Korean Mathematical Society JKMS

Let $M$ be a Riemannian manifold with asymptotically non-negative curvature. We study the asymptotic behavior of the energy densities of a harmonic map and an exponentially harmonic function on $M$. We prove that the energy density of a bounded harmonic map vanishes at infinity when the target is a Cartan-Hadamard manifold. Also we prove that the energy density of a bounded exponentially harmonic function vanishes at infinity.

Keywords: harmonic maps, Bochner type formula, Liouville theorem, Hessian comparison theorem

MSC numbers: 53C43, 58E20