English

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.

Keywords

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

R2 v1 2026-06-28T09:43:05.062Z