Partial regularity of mass-minimizing rectifiable sections |
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Authors: | David L. Johnson Penelope Smith |
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Affiliation: | (1) Department of Mathematics, Lehigh University, 14 E. Packer Avenue, Bethlehem, Pennsylvania, 18015-3174, U.S.A. |
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Abstract: | Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold M n. 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. Theorem 1. For any homology class of sections of B, there is a mass-minimizing rectifiable current T representing that homology class which is the graph of a C1 section on an open dense subset of M. Mathematics Subject Classifications (2000): 49F20, 49F22, 49F10, 58A25, 53C42, 53C65. |
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Keywords: | Geometric measure theory Foliations Sections Volume Minimal submanifolds |
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