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cs.CG2022
The medial axis of closed bounded sets is Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms
Hana Dal Poz Kouřimská, André Lieutier, Mathijs Wintraecken
We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let be (fixed) closed set (that contains a bounding sp…
cs.CG2022
Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds
Dominique Attali, Hana Dal Poz Kouřimská, Christopher Fillmore +4
In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work,…
math.CO2022★ 1 cited
Brillouin Zones of Integer Lattices and Their Perturbations
Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +3
For a locally finite set, , the -th Brillouin zone of is the region of points for which is the -th smallest…