Estimating the reach of a submanifold

Abstract: The reach is an important geometric invariant of submanifolds of Euclidean space. It is a real-valued global invariant incorporating information about the second fundamental form of the embedding and the location of the first critical point of the distance from the submanifold. In the subject of geometric inference – estimating the geometry from samples of points drawn from the manifold - the reach plays a crucial role. I will give a new method of estimating the reach of a submanifold, developed jointly with Clément Berenfeld, Marc Hoffmann and Krishnan Shankar. This results in improved convergence rates, but a minimax optimal estimator remains to be found.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

Irish Geometry Seminar