Asymptotic properties of energy of harmonic maps on asymptotically hyperbolic manifolds

摘要

Asymptotic behavior of energy of a harmonic map defined on an asymptoticallyhyperbolic manifold is considered. Using the growth of energy, we show that aharmonic map defined on some asymptotically hyperbolic manifolds has to beconstant if the total energy is finite, or if the map approaches a point fastenough, in terms of a defining function for the boundary.