Partial regularity of mass-minimizing Cartesian currents
Differential Geometry
2008-07-17 v4 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.math/0403483,
title = {Partial regularity of mass-minimizing Cartesian currents},
author = {David L. Johnson and Penelope Smith},
journal= {arXiv preprint arXiv:math/0403483},
year = {2008}
}
Comments
36 pages, no figures. Published version, with minor revisions from previous arxive version