Partial regularity of mass-minimizing rectifiable sections

Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold Mn. There is a natural Riemannian metric on the total space B consistent with the metric on M. With respect to that metric, the volume of a rectifiable section σ: M → B is the mass of the image σ(M) as a rectifiable n-current in B.