Harmonic maps versus Poisson equations on noncompact Riemannian manifolds (Q2721949)

Suppose there is a map \(v\) from a noncompact Riemannian manifold \(M\) into a nonpositively curved Riemannian manifold \(N\) so that the Poisson equation on the domain manifold given by NEWLINE\[NEWLINE - \Delta U = |\tau(v)|NEWLINE\]NEWLINE has a solution, with \(\tau(v)\) being a tension field. Then there exists a harmonic map. Similar to the work of \textit{S. Bando} [The existence theorem of Harmonic objects via Green function. The third Pacific Rim Geometry Conference (Seoul 1996), International Press, 1-6 (1998; Zbl 1010.53051)], on the basis of this observation, the author re-examined some results of the previous work of Li and Tam, seeking for further developments.