Partial Regularity of Mass-minimizing Cartesian Currents
نویسنده
چکیده
Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold M. 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. For any homology class of sections of B, there is a mass-minimizing Cartesian current T representing that homology class which is the graph of a C section on an open dense subset of M .
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