Optimal regularity of harmonic maps from a Riemannian manifold into a static Lorentzian manifold

Abstract

In this paper, we give an optimal regularity result for some class of weakly harmonic maps from a Riemannian manifold M into a static Lorentzian manifold. Our main result is the following: For such class of weakly harmonic map w, there exists closed set M such that w is C 1 in Mn and the Hausdor dimension of is less than or equal to dimM 3.