PARTIAL REGULARITY OF HARMONIC MAPS FROM A RIEMANNIAN MANIFOLD INTO A LORENTZIAN MANIFOLD

摘要

We study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map (u, v) from a smooth bounded open domain ??R~m to a Lorentzian manifold with Dirichlet boundary condition, we prove that it is smooth outside a closed set whose (m-2)-dimensional Hausdorff measure is zero. Moreover, if the target manifold N does not admit any harmonic spheres S~l, l = 2,...,m-1, we show (u, v) is smooth.