Partial regularity for weak heat flows into riemannian homogeneous spaces

Abstract

It is proved that any weak flow of harmonic maps into a compact homogeneous manifold satisfying the monotonicity inequality and the energy inequality is regular off a closed set of m-dimensional Hausdorff measure zero (w.r.t parabolic metric), and coincides with a regular flow if the latter one exists. Moreover, it is also shown that the weak limit of a sequence of such weak flows is a weak flow.