Communications in Analysis and Geometry

Volume 16 (2008)

Number 4

Homotopy problems for harmonic maps to spaces of nonpositive curvature

Pages: 681 – 733



Bent Fuglede (Universitetsparken, Copenhagen)


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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