Mathematics

I present some existence results for p-harmonic maps in homotopy classes of maps between nonsmooth spaces. The subject started with the seminal work of Sampson-Eells in the sixties with manifolds. It has since evolved through contributions from Fuglede, Gromov, Schoen, Korevaar, Jost and many others to nonsmooth spaces. A standard assumption (to ensure a satisfactory theory) is that the target space exhibits some nonpositive curvature. I will work with maps of finite energy between a Poincaré space and a locally CAT(0) space and describe an existence result as well as challenges in working with nonsmooth spaces.