2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152178Asymptotic behavior of energy of a harmonic map defined on an asymptotically hyperbolic manifold is considered. Using the growth of energy, we show that a harmonic map defined on some asymptotically hyperbolic manifolds has to be constant if the total energy is finite, or if the map approaches a point fast enough, in terms of a defining function for the boundary.LaTeX, 17 pagesDifferential Geometry58E20 (Primary) 58G03 (Secondary)text