Partial regularity of massminimizing Cartesian currents
Abstract
Let B be a fiber bundle with compact fiber F over a compact Riemannian nmanifold 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 ncurrent in B. Theorem: For any homology class of sections of B, there is a massminimizing Cartesian current T representing that homology class which is the graph of a C^1 section on an open dense subset of M.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:math/0403483
 Bibcode:
 2004math......3483J
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs;
 49F20;
 49F22;
 49F10;
 58A25;
 53C42;
 53C65
 EPrint:
 36 pages, no figures. Published version, with minor revisions from previous arxive version