ASYMPTOTIC BEHAVIOR OF HARMONIC MAPS AND EXPONENTIALLY HARMONIC FUNCTIONS

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.