Varifolds represent a natural generalization of manifolds in the measure theoretic sense, they encode a joint distribution of mass and tangents and were introduced mainly as a model for soap films and to solve the plateau problem.
In this talk, we will present recent works of Buet, Leonardi and Masnou on the geometry of varifolds (definition of weak curvatures) with a particular focus on point cloud varifolds, at last we will give a glimpse of how to define a consistent Laplace operator for general measures.