We use geometric measure theory to introduce the notion of asymptotic conesassociated with a singular subspace of a Riemannian manifold. This extends theclassical notion of asymptotic directions usually defined on smoothsubmanifolds. We get a simple expression of these cones for polyhedra in E^3,as well as convergence and approximation theorems. In particular, if a sequenceof singular spaces tends to a smooth submanifold, the corresponding sequence ofasymptotic cones tends to the asymptotic cone of the smooth one for a suitabledistance function. Moreover, we apply these results to approximate theasymptotic lines of a smooth surface when the surface is approximated by atriangulation.
展开▼
