Work

Isotropic constants and regular polytopes

Year: 2025

Type: article

Abstract: We discuss first-order optimality conditions for the isotropic constant and combine them with RS-movements to obtain structural information about polytopal maximizers. Strengthening a result by Rademacher, it is shown that a polytopal local maximizer with a simplicial vertex must be a simplex. A similar statement is shown for a centrally symmetric local maximizer with a simplicial vertex: it has to be a cross-polytope. Moreover, we show that a zonotope that maximizes the isotropic constant and that has a cubical zone must be a cube. Finally, we consider the class of zonotopes with at most n + 1 generators and determine the extremals in this class.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110361

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: $3,790

Funders: Deutsche Forschungsgemeinschaft, Berlin Mathematics Research Center MATH+