HARMONIC MAPS VERSUS POISSON EQUATIONS ON NONCOMPACT RIEMANNIAN MANIFOLDS

1.Introducti0llStartingfromtheworkofP.LiandT.F.Taml1'2])therearesomeprogressonthestudyofharmonicmaPsbetweennegativelycurvedc0mplete,noncompactriemannianmanifolds.Wemayquote2-5]justforafew.Thenewstartingpoilltin1]isthea-ssumption0fagivenmaPwithitstensi0nfieldinasuitableSob0levspace.Asacomparison,wementi0nthatthekeytechniqueofthemethod0fEells-Sampsonl6]istheuseofaBochnertypeevoluti0n0ftheenergydensitywithaninitialdataoftotalenergy.InthispaPer,wetrytogivealargec1assofapprokimateharmonicma…

HARMONIC MAPS VERSUS POISSON EQUATIONS ON NONCOMMCT RIEMANNIAN MANIFOLDS

Suppose there is a map from a noncompact riemannian manifold into a nonpositively curved riemannian manifold such that its tension field is in a suitable Banach space. Then there exists an intimate relationship between harmonic maps and Poisson equations on the domain manifold. On the basis of this observation, we can extend some results of the previous work of Tam and Li.