Boundary regularity for weak heat flows

The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold M with boundary into general compact Riemannian manifold N without boundary is considered. It is shown that the singular set Sing(u) of the weak heat flow satisfies H-rho(n)(Sing(u)) = 0, with n = dimensionM. Here H-rho(n) is Hausdorff measure with respect to parabolic metric P((x, t), (y, s)) = m-(\x -y\, root\t-s\).