Work

Small perturbations of polytopes

Year: 2024

Type: article

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.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2024.110644

Author: Christian Kipp

Institution: Technische Universität Berlin

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,670

Funder: Deutsche Forschungsgemeinschaft