Homotopy problems for harmonic maps to spaces of nonpositive curvature

Two results by N.J. Korevaar and R.M. Schoen (1993) aboutsolvability of the free homotopy problem and the Dirichlethomotopy problem for harmonic maps from a compactRiemannian manifold $X$ to a compact geodesic space $Y$ ofnonpositive curvature are strengthened here, and extended,particularly by allowing $X$ to be any compact admissibleRiemannian polyhedron. In that setting, the two resultswere stated in the author's monograph from 2001 with J.Eells, but the short proofs given there were incomplete.

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Published 1 January 2008