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math.MG2024
On exact covering with unit disks
Ji Hoon Chun, Christian Kipp, Sandro Roch
We study the problem of covering a given point set in the plane by unit disks so that each point is covered exactly once. We prove that 17 points can always be exactly covered. On…
math.MG2023★ 2 cited
Small perturbations of polytopes
Christian Kipp
Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a f…
math.MG2022
Affine Subspace Concentration Conditions for Centered Polytopes
Ansgar Freyer, Martin Henk, Christian Kipp
Recently, K.-Y. Wu introduced affine subspace concentration conditions for the cone volumes of polytopes and proved that the cone volumes of centered, reflexive, smooth lattice pol…