Approximate curvatures of a varifold
Prof. Gian Paolo Leonardi, Università di Trento.
Aula Beltrami, Dipartimento di Matematica – Mercoledì 15 Maggio 2019 h.15:00
Abstract. Varifolds, i.e. Radon measures on the Grassmannian bundle of (unoriented) d-tangent planes of a Riemannian n-manifold M, represent a variational generalization of d-dimensional submanifolds of M. By suitably revisiting Hutchinson’s definition of generalized second fundamental form, we propose a notion of approximate second fundamental form that is well-defined for general varifolds. Rectifiability, compactness, and convergence results are proved, showing in particular the consistency and stability of approximate curvatures with respect to varifold convergence. If restricted to the case of “discrete varifolds”, this theory provides a general framework for extracting geometric features from discrete datasets. Some numerical tests on point clouds, also showing the robustness with respect to noise, will be shown. This is a joint research with Blanche Buet (Univ. Paris XI – Orsay) and Simon Masnou (Univ. Lyon 1).