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 s:M--> B is the mass of the image s(M) as a rectifiable n-current in B. Theorem: 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^1 section on an open dense subset of M.
arXiv Mathematics e-prints
- Pub Date:
- March 2004
- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs;
- 36 pages, no figures. Published version, with minor revisions from previous arxive version