SOME EXISTENCE THEOREMS FOR HARMONIC MAPS IN RIEMANNIAN MANIFOLDS

In this paper, the harmonic maps into the Riemannian manifolds without focal points are con-sidered. Their existence for boundary value problem is obtained. By using the regularity theorem,recently established by R. Schoen and K. Uhlenbeek, the problem is transformed into nonexistencefor certain special harmonic maps. We proved such a nonexistence, then proved main results in thispaper by usual procedure of the direct method of the calculus of variations.