HARMONIC MAPS ON SPACES WITH CONICAL SINGULARITIES

Let X = X(m+1) be a compact metric space with conical singularities SIGMA : then X - SIGMA is an open, (m + 1)-dimensional Riemannian manifold dense in X. Let N be a compact Riemannian manifold; we say that a map f : X --> N is harmonic if f is continuous and its restriction to X - SIGMA is harmonic in the usual sense. We apply heat flow techniques to prove an existence result for nonpositively curved N. In dimension 2, our results hold for conformally conical singularities and lead us to an existence theorem for complex projective algebraic curves.