Discretization and Approximation of Surfaces Using Varifolds

We present some recent results on the possibility of extending the theory of varifolds to the realm of discrete surfaces of any dimension and codimension, for which robust notions of approximate curvatures, also allowing for singularities, can be defined. This framework has applications to discrete and computational geometry, as well as to geometric variational problems in discrete settings. We finally show some numerical tests on point clouds that support and confirm our theoretical findings.