Calculus of Variations and Geometric Measure Theory

S. Baldo - G. Orlandi

Fiber bundles and regular approximation of codimension-one cycles

created on 29 Jan 2002


Published Paper

Inserted: 29 jan 2002

Journal: Ann. Global Anal. Geom.
Volume: 20
Number: 1
Pages: 47-57
Year: 2001


We derive an approximation of codimension-one integral cycles (and cycles modulo $p$) in a compact riemannian manifolds by means of piecewise regular cycles: we obtain both flat convergence, and convergence of the masses. The theorem is proved by using suitable principal bundles with discrete group. As a byproduct, we give an alternative proof of the main results in BO1, BO2, which does not use the regularity theory for homology minimizers in a riemannian manifold. This gives also a result of $\Gamma$-convergence.

Keywords: Geometric measure theory, minimal surfaces, $\Gamma$ - convergence, homology groups, fiber bundles