EXISTENCE OF HOMOTOPIC HARMONIC MAPS INTO METRIC SPACE OF NONPOSITIVE CURVATURE

EXISTENCE OF HOMOTOPIC HARMONIC MAPS INTO METRIC SPACE OF NONPOSITIVE CURVATURE

The definitions and techniques, which deals with homotopic harmonic maps from a compact Riemannian manifold into a compact metric space, developed by N. J. Korevaar and R. M. Schoen [7] can be applied to more general situations. In this paper, we prove that for a complicated domain, possibly noncompact Riemannian manifold with infinitely generated fundamental group, the existence of homotopic harmonic maps can be proved if the initial map is simple in some sense.

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