Affine Subspace Concentration Conditions for Centered Polytopes

TL;DR

This paper extends affine subspace concentration conditions, initially proven for centered, reflexive, smooth lattice polytopes, to all centered polytopes, broadening the scope of these geometric constraints.

Contribution

The paper generalizes affine subspace concentration conditions from specific classes of polytopes to all centered polytopes, enhancing understanding of their geometric properties.

Findings

Affine subspace concentration conditions hold for all centered polytopes.

Extension of Wu's results beyond reflexive, smooth lattice polytopes.

Broader applicability of cone volume inequalities.

Abstract

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 polytopes satisfy these conditions. We extend the result to arbitrary centered polytopes.