Affine subspace concentration conditions for centered polytopes

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.

The logarithmic Minkowski conjecture and the Lp-Minkowski problem

“…a proper linear subspace L ⊂ R n and a small ε > 0, then K is close to the sum of two complementary lower dimensional compact convex sets according to Böröczky, Henk [47]. We note that Freyer, Henk, Kipp [109] even verified certain so-called Affine Subspace Concentration Conditions for the cone volume measure of centered polytopes.…”