OPTIMAL REGULARITY OF HARMONIC MAPS FROM A RIEMANNIAN MANIFOLD INTO A STATIC LORENTZIAN MANIFOLD

摘要

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 Sigma subset of M such that w is C-infinity in MSigma and the Hausdorff dimension of C is less than or equal to dim M - 3. [References: 13]