Minimising currents and the stable norm in codimension one

Abstract

We analyse the structure of locally minimising closed (n−1)-currents in an n-dimensional Riemannian manifold M. In particular, we prove that such currents are measured laminations by (possibly singular) minimal hypersurfaces. We use ideas from the theory of codimension one singular foliations to decompose these currents. The results are used to investigate the stable norm on $\text{H}{}_{\mathrm{n-1}}\text{(M,}\text{R}\text{)}$.