Harmonic maps from surfaces to \(\mathbb{R}\)-trees (Q1895761)

Certain geometric applications have led Corlette and Gromov to the problem of the existence of harmonic maps of Riemannian manifolds \(M\) into geodesic spaces \(Y\) of nonpositive curvature. That is an attractive generalization of the existence theorem in case \(Y\) is a Riemannian manifold. Their applications [\textit{K. Corlette}, Ann. Math., II. Ser. 135, No. 1, 165-182 (1992; Zbl 0768.53025); and \textit{M. Gromov} and \textit{R. Schoen}, Publ. Math. Inst. Hautes Etud. Sci. 76, 165-246 (1992)] are rather esoteric. The present author gives several direct -- and lovely -- applications to Riemann surfaces with measured foliations \(\mathcal F\). Here \(Y\) is a 1- dimensional geodesic space associated to \(\mathcal F\).