The canonical lamination calibrated by a cohomology class

Let \(M\) be a closed oriented Riemannian manifold of dimension \(d\), and let \(\rho \in H^{d - 1}(M, \mathbb R)\) have unit norm. We construct a lamination \(\lambda_\rho\) whose leaves are exactly the minimal hypersurfaces which are calibrated by every calibration in \(\rho\). The geometry of \(\lambda_\rho\) is closely related to the the geometry of the unit ball of the stable norm on \(H_{d - 1}(M, \mathbb R)\), and so we deduce several results constraining the geometry of the stable norm ball in terms of the topology of \(M\). These results establish a close analogy between the stable norm on \(H_{d - 1}(M, \mathbb R)\) and the earthquake norm on the tangent space to Teichm\"uller space.