Homotopy problems for harmonic maps to spaces of nonpositive curvature

摘要

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