Stable norms of surfaces: local structure of the unit ball at rational directions (Q1380460)

The author considers the stable norm defined by Federer [\textit{M. Gromov}, `Structures métriques pour les variétés riemanniennes', Cedic, Paris (1981; Zbl 0509.53034), pp. 50-51] in \(H_q(M, \mathbb{R})\), where \(M\) is a compact manifold equipped with a smooth Riemannian metric. He establishes that if \(q=1\) and \(M\) is a closed orientable surface with a smooth Finsler metric, then this norm is neither strictly convex nor smooth.