# Harmonic maps between singular spaces

Bent Fuglede
(KU)
Analysis Seminar
Thursday, 4 March, 2010, at 16:15, 1110-223
Abstract:
This is an overview of my study during the passed decade of harmonic maps from an admissible Riemannian polyhedron to a complete geodesic space of nonpositive curvature, beginning in cooperation with the late Professor James Eells. After describing the classical setting, in particular the Eells-Sampson existence theorem (1964), harmonic maps are defined in the stated more general setting as continuous local energy minimizers. Harmonic maps are shown to be Hölder continuous, and the variational Dirichlet problem is solved. Finally, the Eells-Sampson theorem is extended to this setting, asserting that every continuous map is homotopic with a harmonic map.
Contact person: Bent Ørsted