Small perturbations of polytopes
Metric Geometry
2024-09-06 v2 Functional Analysis
Abstract
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 full characterization of the set of realizable perturbations if the perturbed body is a polytope. As an application, we derive a necessary condition for polytopal maximizers of the isotropic constant.
Cite
@article{arxiv.2303.18033,
title = {Small perturbations of polytopes},
author = {Christian Kipp},
journal= {arXiv preprint arXiv:2303.18033},
year = {2024}
}
Comments
30 pages, 3 figures, accepted manuscript